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Author
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Topic: Virtues of Scientists
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Christopher M. Langan
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Member # 264
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posted 23. April 2003 18:33
The first thing that any scientist must understand about modeling is that some models are optional, while some are not. As Kant and others have reminded us, among those that are not are basic categories of cognition and perception. Because the arithmetical operation of addition corresponds to disjoint union of sets, and because the proposed experiment involves taking a disjoint union of sets - that's what adding objects to a set of other objects is necessarily about - addition qualifies as an irreducible category of perception with respect to it. So one need merely run the associated gedankenexperiment subjectively, and nature must objectively conform to the outcome.
In other words, to add marbles to a set of other marbles is to create a disjoint union of sets with cardinality the sum of their cardinalities, and one can do this entirely in one’s head. No physical experiment is required. If it were, then scientists would be so limited in their power to hypothesize and theorize that they could not function. Because necessary configurations of essential categories of cognition and perception are also necessary features of objective reality, scientists cannot rule out the mathematical (rational, subjective) derivation of nontrivial facts of nature.
Unfortunately, certain possibilities of this kind are in fact ruled out by the empirical methodology of mainstream science. This exemplifies the danger of dismissing philosophy as "irrelevant to science". In my opinion, scientists who do not make this particular error of conceptualization are exhibiting a most admirable and important intellectual virtue.
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Nel
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posted 23. April 2003 19:23
RBH writes:
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I spent 10 years putting together data (both reviewed in existing literature and data I generated in my own research) and getting it into a form that (with help from a sympathetic editor) was publishable. Ten years.
I think that's pretty ridiculous and completely unnecessary if you ask me. Now, imagine what your paper may be today, if instead of 10 years of trying to get that paper into a publishable form with only you and a "sympathetic" editor at your side, you already had it published and instead had 10 years of something like this:
quote:
To make the peer review system more transparent, some leading medical journals, such as the British Medical Journal, are exploring open peer review, in which manuscripts are posted on the Internet, along with signed reviews and comments from third party interests.
Recent Article On Peer Review
With an idea such as Mike's cytosine deamination/IHE stuff such a process is ideal.
[ 23. April 2003, 19:39: Message edited by: Nelson_Alonso ]
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gedanken
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posted 23. April 2003 20:06
Chris Langham said:
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My point, of course, was that one can establish truth in nature by mathematical as well as scientific means. For example, in order to prove that 2+2=4 in nature, one doesn’t need to run an experiment in which one puts two marbles in an empty glass jar, peers inside, adds two more and then runs a final count. One can simply use arithmetic and count on nature (pun intended) to follow suit. Scientists have no good reason to assume that nothing of this nature is possible in the more advanced realms of logic and mathematics. So although some ID hypotheses may indeed be empirically testable, mathematical verification may be more appropriate for others.
RBH gave a good example. Here is another:
We have Euclidean geometry as one of the oldest mathematical proofs. Isn’t that good enough for us to know that Euclidean geometry is completely accurate for astronomical measurements and models? Surely we can observe the accuracy of that mathematical construct here on earth. “One can simply use” that experience with Euclidean Geometry and its proofs, “and count on nature … to follow suit.”
But wait? Do we possibly need to do a little testing to determine if nature actually obeys our claim? Or isn’t armchair philosophy sufficient for analysis of nature? I would argue that if armchair philosophy was sufficient for analysis of nature, we would still be using an Aristotelian view of how nature works. But instead people slowly learned the modern empirical techniques. The methods of actually checking our claims carefully with observation in various forms has served very well -- that is why science is so successful and armchair philosophy is not so successful in subject matters of the actual workings of the actual physical world.
quote:
Because the arithmetical operation of addition corresponds to disjoint union of sets, and because the proposed experiment involves taking a disjoint union of sets - that's what adding objects to a set of other objects is necessarily about - addition qualifies as an irreducible category of perception with respect to it. So one need merely run the associated gedankenexperiment subjectively, and nature must objectively conform to the outcome.
This is more of the very same subject I mentioned above. One only needs to run the gedanken experiment (a favorite topic of mine) to see that Euclidean geometry must be true and should be valid everywhere, “and nature must objectively conform to the outcome.” (???)
Of course another case dealing with sets: Different species are clearly disjoint sets. So evolution by small changes clearly (logically) cannot produce new species, because each descendent that is only slightly different from the parent is clearly a member of the same set. We observe small differences in individuals within a species, and that difference does not qualify as a marker of membership in a different species set. “So one need merely run the associated gedanken experiment subjectively, and nature must objectively conform to the outcome.” Darwinian evolution is disproved while sitting in my armchair! No need to observe nature any further.
Clearly from what some people seem to think, the virtue of scientists carefully checking claims against observation of nature is not necessary.
[ 23. April 2003, 20:17: Message edited by: gedanken ]
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RBH
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posted 23. April 2003 20:41
Chris Langan wrote quote:
In other words, to add marbles to a set of other marbles is to create a disjoint union of sets with cardinality the sum of their cardinalities, and one can do this entirely in one's head. No physical experiment is required. If it were, then scientists would be so limited in their power to hypothesize and theorize that they could not function. Because necessary configurations of essential categories of cognition and perception are also necessary features of objective reality, scientists cannot rule out the mathematical (rational, subjective) derivation of nontrivial facts of nature.
One doesn't rule them out out of hand or a priori; I agree that would be irrational and unproductive. The point of the little marble-dumping thought exercise was to illustrate the point that mapping the terms and operators of math into the objects, processes, and operations of the world is not automatic, unquestionable, or given; it must be thought through and justified, not merely assumed. In fact, Langan's identification of the arithmetical operation of taking a joint set with the physical operation of dumping two bunches of marbles together is just that kind of justification: it establishes a mapping between the arithmetic and the physical operations. That is precisely my point: that mapping must be justified.
In other situations the correspondence of model and physical world is not so obvious. In some cases we don't even know the appropriate math and hence must use other kinds of models to help our understanding. In every case of modeling, mathematical or not, the correspondence between model and physical world is critical and cannot be taken as a given without examination. That does not at all limit the power of scientists to hypothesize and theorize, but it does constrain claims about the validity or truth value of those hypotheses unless and until the correspondence relations have been closely examined and justified. Once again, that's why science is science rather than philosophy: that last step of testing the correspondences hypothesized by looking for the new observations the model predicts should be made.
I'm not sure Langan and I actually disagree all that much. I doubt that Langan is arguing that testing hypotheses is irrelevant or a waste of time. Where we may disagree is in the necessity of taking some models as non-optional and therefore apparently not accessible to evaluation and testing. Kant notwithstanding, I haven't seen a convincing argument to that effect, and I'm certainly not going to accept it as some sort of a priori truth. In particular, just what the "necessary categories of cognition and perception" might be is not at all obvious or universally agreed. I'm pretty sure they can't be satisfactorily described by the unaided examination of one's mental innards.
RBH
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Christopher M. Langan
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posted 23. April 2003 20:49
Gedinken wrote:
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RBH gave a good example. Here is another: We have Euclidean geometry as one of the oldest mathematical proofs. Isn’t that good enough for us to know that Euclidean geometry is completely accurate for astronomical measurements and models?
First, although RBH’s handling of my example is interesting and even somewhat instructive, I’ve already explained why it doesn’t vindicate your blanket approval of standard scientific methodology. Second, your current example differs from my example in a crucial way: it crosses the line into the domain of what would, for reasons of ignorance, currently be considered "optional" models. Thus, while the answer to your question is negative - at least at the current stage of the geometric modeling of nature – this, along with your oversimplified "disproof" of Darwinism, still fails to validate your position. So if you mean to compare your new examples to 2+2=4, I’m afraid that won't work. My point only required one valid example, and I gave it.
Note the italics in the above paragraph. Their purpose is to point out that once again, you have no way of knowing whether or not the proper geometry for astronomical applications cannot be mathematically deduced, particularly in the long run. The conventional working assumption, of course, is "no, it can’t!" But a working assumption is not necessarily a truth, and a scientist asked to prove this assumption wouldn’t even know where to begin. (Fortunately, this need not apply to everyone for all time.)
[ 23. April 2003, 20:51: Message edited by: Christopher M. Langan ]
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RBH
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posted 23. April 2003 21:22
Now we come to the nub. Langan wrote quote:
Their purpose is to point out that once again, you have no way of knowing whether or not the proper geometry for astronomical applications cannot be mathematically deduced, particularly in the long run.
First, he's right: one has no way of knowing whether the proper geometry cannot be mathematically deduced. Two considerations merit attention, though. The first is that I very much doubt that any such deduction can follow from free-floating premises, premises that have no tested correspondences with the physical universe. If the premises have no known and tested correspondence relations with the physical universe, then any conclusion that is reached through the purely syntactic mathematical manipulations of symbols is uninterpretable, and the deduction is quite literally about nothing.
Second, assume for the moment that one has deduced a candidate for the title "proper geometry for astronomical observations" from premises that have some anchoring in tested correspondences with the physical universe. How will one know that candidate is not merely a candidate but is in fact the 'real' proper geometry? My very strong opinion is that some clever scientists will figure out observational consequences that differentiate that candidate from other candidates, and go look for them. That is, there will be empirical research to determine the truth value of the claim "This is the proper geometry."
RBH
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gedanken
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posted 23. April 2003 22:13
I’m going to say something that at least slightly conflicts with my previous posts. But I still disagree largely with Chris.
I think that the concept of numbers is induced, not deduced. [* * * * = * * + * *] The symbols 2 and 4 were names given, not mathematical concepts from some sort of logic or proof. The experience of sets and primitive arithmetic operations are some of our first marginally scientific observations of nature. But it is the consistency of mixing sets of small counts that shows the correctness and usefulness of the mathematics, not the other way around. We inductively observe the correctness of mathematics from experience. We deduce logically certain principles of mathematics, by making postulates and arguing logically from those postulates. But yet the very properties of logic itself are inductively learned concepts. We see that those principles regularly hold when applied to the world around us -- indeed categorization of objects and simple set operations with those objects is an observed property of nature. So in a sense, 2 + 2 = 4 is an observed property of nature. Where I disagree with Chris is that is not deduced logically, rather logic and that property are inductively learned from experience in a very early and fundamental application of the same principles as are the basis of science.
(In this sense mathematics is part of science. But it does not give freedom to rely on deduction rather than careful verification by observation of physical world when applied as claims about the physical world.)
On the geometry of the universe:
One could never “deduce” that property without it being based on some observation that is not primitive of the baby’s ability to think. Rather that would be based on some form of repeated experience learned in life’s experience. Such life’s experience, when found repeatedly consistent, would have the same property as other scientific observation. So if a geometric property of the universe were deduced it would not be of pure thought, rather it would simply be an observation of a logical consistency of a deduction from other inductively observed principles. No deduction occurs without starting with the postulates or primitive concepts from which the deduction proceeds. The postulates are the observed aspect of nature that are checked for consistency. (Furthermore there are always hidden postulates, e.g. the rules of logic themselves that are used. Geometric proofs contain more assumptions than actually are shown as “postulates.”) But if inconsistency is found with observation in nature, then either the postulates, or the logic must be at fault. Deductive reasoning may not be at fault in such a failure, rather the assumption of the postulates themselves, or the assumption that the logic related in the ‘proof’ was correct, is what is questioned when an inconsistency of scientific principle is found with observation of nature.
The genesis in those “other inductively observed principles” still makes the “deduced” geometric properties have a scientific basis in observation of nature -- and furthermore we would never know that was correct until we observed consistency with nature over time. Thus no matter how much deduction is involved, it is the observation of consistency with nature that is paramount.
The virtue of careful and methodical verification of claims about nature is a principle virtue of scientists. Honesty is upheld by communication wherein others can verify the consistency of substantial portions for themselves. It upholds the virtue of careful communication of those results from careful and methodological verification. It is an aspect of modern rationality that is an important part of modern life for me -- I don’t want the world to backtrack on the importance of rationality. It can happen.
[ 23. April 2003, 22:37: Message edited by: gedanken ]
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Alix Nenuphar
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posted 23. April 2003 23:08
I believe it is important to recognize that virtually all models which purport to represent 'reality' are parameterized: that certain values representing empirical fact define the model, and those values cannot be generated by the model itself. (Dr. Dembski reminded me of this fact in his recent thread regarding the applicability of Gödel's Theorem to evolution and ID.) The gravitational constant, the fine-structure constant, the number and masses of leptons and baryons, etc. cannot be generated from within purely philosophical systems.
It might be argued that this is a naïve view; that in a wholly deterministic universe such data representing historical contingency are derivable given perfect calculation and perfect knowledge of initial conditions - but empirical data shows this to be impossible - our understanding of the initial conditions is guaranteed incomplete, Gödel's Theorem guarantees our models are incomplete, and available computing power limits our ability to generate what data we can derive.
Which brings me to my final point: that science is, at heart, a pragmatic discipline, and there is a considerable reduction in cost achieved by empirical data collection, rather than philosophical data generation.
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Christopher M. Langan
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posted 24. April 2003 06:53
quote:
I think that the concept of numbers is induced, not deduced. [* * * * = * * + * *] The symbols 2 and 4 were names given, not mathematical concepts from some sort of logic or proof.
This appears typical of a viewpoint called nominalism, which ignores the necessity for something general enough to correlate and enforce consistency among instances of perception. Nominalism leads to an unanswerable question: what accounts for the consistency of percepts to which the same names are consistently given (and from which babies learn by induction)? Nominalism is often juxtaposed with realism, which holds that universals exist. Realism is in some sense true, for if universals did not exist, then the universe would have no means of enforcing its own universal self-consistency. As it happens, this has a technical formulation: if the universe were a language (and the program of scientific theorization attests that it can be so-represented for scientific purposes), then abstract truths like 2+2=4 would constitute its "syntax", and if categories of perception and cognition were not to match this syntax, then the consistency of the universe would not be reflected in perception and science would be impossible. On the other hand, if this kind of syntax were really learned by induction, then the mind of an observer would be free to construct alternative syntaxes. If this were possible with respect to arithmetic, then one could (e.g.) devise new integer sequences with different distributions of primes. If you think that this is feasible, then go ahead and try it...but don’t be too surprised if it turns out to be a bit harder than expected.
Since you continue to focus on the example of Euclidean geometry, a couple of observations may be in order. In classical mechanics, the geometry of the universe was assumed to be flat; Special Relativity merely updated the flatness concept to four dimensions. Then came General Relativity, which replaced the flat Minkowskian manifold of Special Relativity with the concept of curved spacetime. But this raised a question: with respect to what is spacetime curved? In answering this question, we find that the microscopic geometry of nature is still assumed to be flat; the flat Minkowskian manifold has simply become the local (tangent space) limit of a curved Riemannian manifold. In effect, flat "ideal geometry" remains that on which curved physical geometry is defined. To complicate things yet further, whereas geometry was once considered the basic stuff of which the universe is made, this notion has led to intractable theoretical problems and is no longer on firm footing. It now seems that geometry must be replaced with something more fundamental, raising the possibility that the replacement operation will determine certain geometric particulars of nature without benefit of observation.
Regarding Alix’s post, I’m not arguing that undecidable features of nature do not exist; in fact, their existence would imply the correctness of a certain model of nature and causality with which I happen to be associated (because undecidability is a formal property, and formal is roughly synonymous with linguistic, objectively undecidable elements in nature would imply that nature is linguistic in character). What I do argue is that among the features of nature that are not undecidable, some may be amenable to a priori investigation, and among those that are, some may be at least partially determined by volition.
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gedanken
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posted 24. April 2003 10:29
quote:
This appears typical of a viewpoint called nominalism, which ignores the necessity for something general enough to correlate and enforce consistency among instances of perception. Nominalism leads to an unanswerable question: what accounts for the consistency of percepts to which the same names are consistently given (and from which babies learn by induction)? Nominalism is often juxtaposed with realism, which holds that universals exist. Realism is in some sense true, for if universals did not exist, then the universe would have no means of enforcing its own universal self-consistency.
I need to emphasize most strongly that I am not advocating nominalism, quite the opposite. (How can I put that in language that is stronger -- I can’t think of any useful way except to continue!) That some concept is induced rather than deduced bears not on whether it is a general property of reality!
My point will be in agreement with Chris here. The experience upon which mathematics is based has some “true” basis in the real world. It is not a feature of our minds, it is a feature of the real world as comprehended by our minds. When we “add” objects (or combine sets) those objects or sets are mental states that represent the real world agglomerations of mass or substance that are being combined. A naïve realism (the basic foundation of science) combined with our experience shows that the basics of mathematics have strong foundation in the real world.
My point is that we learn this from the real world! (Thus consistent with above point by Chris). And in that sense, mathematics itself is “scientific” -- once again agreeing in a sense with Chris’s original point of mathematics being part of science.
A couple of links on Realism, Nominalism, Conceptualism, and Greek philosophy: here and here. Aside from an emphasis on a naïve realism, I don’t take a particular position on realism, nominalism, etc., with respect to science. For example it matters not whether the apparently real world is a feature of our minds -- one that is consistent -- because the properties of that consistency studied in science would be the same no matter which the case in that regard.
Where I am disagreeing with Chris is in the earlier post in which Chris appeared to emphasize the deducing of a concept (such as a geometric notion of the universe might be “deduced”) which did not require verification by careful observation of nature. The notion that some things are so obvious that we don’t need to check them carefully by methodical observation of nature, that they can be taken for granted. Science has shown over and over that “common sense” may not give a correct result.
This is where the virtue of scientists carefully and methodically verifying concepts with observation of the real world is so important!
Of course Euclidean geometry is sufficient for most of physics, and only in General Relativity do we discover a real need for divergence (pun intended) from Euclidean concepts. In fact even non-Euclidean geometrys rely on mental concepts based in the Euclidean for any visualization whatsoever of the mathematical symbology. My major point was that in the notion of “common sense”, that one cannot escape the need for careful verification! One cannot simply decry that we can derive the correctness of Euclidean geometry everywhere. We need to continue the program of careful verification with observation. By doing so, we finally realize that Euclidean is not sufficient for all of observation, wherein General Relativity gives geometric concepts that appear to be more consistent with reality.
(And I would note that there are correspondence principles in General Relativity as well as other modern physics branches, in which the more complex reduces to the prior or older and possibly simpler formulation -- even in General Relativity we can have local regions that for all practical purposes obey Euclidean Geometry relations. Thus Special Relativity needs only to be described in terms of Euclidean geometry.)
But I think that while I find that mathematics is derived in part by experience in the real world and usefulness of the basic logic constructs fitting with our experience, I think that operationally mathematics is of earlier and more fundamental foundation. It is not really part of “science” so much as a tool of science. This can be taken as a matter of degree, however. And when a failure is observed, once again one must check for several alternatives. It could be the mathematics itself had an error. It could be that the postulates were not an accurate representation of the real world. It could be that measurements that appeared to diverge were not made correctly according to the promulgated theory. One cannot simply limit which of these is the problem by some sort of declaration. Nor can one simply decry the opposite, that any of the steps is inherently correct. (Thus my examples of Euclidean Geometry, and logical classification of “species” -- both incorrectly formulated postulates in some extension of the reasoning when compared with observed reality.)
Chris, I don’t really have anything in which I disagree with your last post. Rather it seems to be in agreement with my point that careful observation of nature is important, and one can’t simply derive character of nature without the careful methodical verification of the scientific method. That demonstrates the virtue of scientists following those principles.
[ 24. April 2003, 19:02: Message edited by: gedanken ]
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gedanken
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posted 24. April 2003 11:02
quote:
… (because undecidability is a formal property, and formal is roughly synonymous with linguistic, objectively undecidable elements in nature would imply that nature is linguistic in character).
Ah, remember in above the necessity of verification with observations of nature. Certainly our description of nature is linguistic in character. This because all description, even that including visual aides, is interpersonal communication, and such interpersonal communication is largely founded on language.
In our apparent degree of agreement in above post, I note the necessity of careful checking of premises for subtle variances with reality. (For example Euclidean geometry being useful almost everywhere, yet failing in some settings such as the larger picture of the universe.) Likewise the issue of Nominalism you decry above (check my links in last post). How is your claim of principles of linguistic nature holding with observation as implication of an inherent linguistic character not a manifestation of Nominalism?
Or to put it differently, when you extend the theory too far (beyond the limits of applicability) you will note failure in almost any case of any theory. This could be a limitation of linguistic method, rather than a feature of the real universe. (Or such linguistic limitation could be a feature of the real universe, rather than an indication of a linguistic property of the universe per se, taking language as an observed natural property within the universe.)
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