No it would not. Bayes "theorem" is simply a definition for conditioinal probability. It does not really address Ken G point from the perspective of a scientist.Originally Posted by Warren Platts
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No it would not. Bayes "theorem" is simply a definition for conditioinal probability. It does not really address Ken G point from the perspective of a scientist.
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About the only impact Quine had on practicing mathematicians was bringng Tarski to the U.S. Tarski's theorem is of interest.If you like Einstein, you'll love Quine, the philosopher, who famously removed logic and mathematics from the intangible heights of the a priori, back down to the tangible lowlands of the a posteriori--where they belong!
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I will concede that point.
Order of Kilopi
The disquotation theory of truth!
The sentence 'Snow is white' is true if and only if snow is white!
ETA: But hey, Willard Van Orman Quine, from the Philosophy Department at Harvard, has so far, as documented in this thread, alone had impacts on the sciences of: (1) linguistics, (2) anthropology, (3) evolutionary biology, and now (4) mathematics!
Wow!
Not only that, he was discussed in Douglas Hofstadter's one-hit wonder!
Not bad for a philosopher. . . .
Well, since philosophers by definition cannot contribute to science or mathematics, I should rephrase: not bad for a scientist and mathematician!
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No, that was part of Tarski's more useless work in philosophy. It does serve to illustrate my earlier point. Most people would consider the statements "Snow is white" and "It is true that snow is white" to be equivalent without much argument. It takes a philosopher to make a mountain out of this mole hill.
The sentence 'Snow is white' is true if and only if snow is white!
While acting in his capacity as a mathematician Tarski proved that, using the axiom of choice, given a sphere of radius R, and an arbitrary positive number r, one can decompose the first sphere into a finite number of disjoint subsets (exact number not particularly important but as I recall it is 5 or 7) and then by rigid motion place those sets inside a sphere of radius r as disjoint subsets. This is sometimes paraphrased as saying that you could cut up the sun and put it in your pocket.
As you might imagine this was a rather surprising theorem. The trick is that the subsets involved are not measurable, in the sense of Lebesque measure, and hence it makes no sense to talk about the volume of those sets. Among other things, this precludes such a decomposition in the "real world". The main point of the theorem is that it illustrates the non-intuitive conclusions that can be deduced from the axiom of choice, which appears to be intuitively true. Most mathematicians accept and use the axiom in their work, but recognize that it is independent of the other usual axioms of set theory and also that it can have such strange consequences as Tarski's theorem. To quote a professor from years ago regarding this theorem "It just shows that your intuition isn't worth a damn."
So, you see, part-time philosophers are sometimes able to change their hat, act in a different capacity, and produce something with useful content for science or mathematics.
Apologies to Nereid as this is a bit OT, but I couldn't resist the temptation to relate Tarski's theorem since it is rather intriguing. But I will get back on topic.
Order of Kilopi
There's a little bit more to it than that: it's a defense of a mild realism within science.
Right, because neither philosophy per se nor philosophers per se by definition ever produce useful content for science or mathematics. Right? To the extent that Bertrand Russell himself was ever useful, it was to the extent that he was not a philosopher. Am I wrong?
So I take it that your advice for Nereid in her quandary regarding what to do about modified Newtonian dynamics (MOND) or cold dark matter (CMD), is that any recourse to the philosophy of science will be counterproductive. Yes No?
Last edited by Warren Platts; 2008-Jul-28 at 03:26 AM. Reason: replace 'a lot' with 'a little bit'
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One small note: I detect a slight inconsistency with your treatment of names. When I merely use a word like 'theorem' or 'law' just because that's the received usage--right or wrong--you are quick to point out that my choice of words are misleading. But when Nereid, bless her heart, asks what's the difference between 'hypothesis', 'theory', 'model', or 'law', it's like, hey, it doesn't matter what words we use, what's important is the purpose, the usefulness, the content.
But I really am interested for professional reasons why you think that the TBSP correlation coefficients (r2 scores) is a good example of when mathematics and assumptions don't gel. Because I don't see that at all. I'm just trying to understand what you are trying to say here. Your point went right over my head. Could you please be a little more explicit?
Order of Kilopi
You mistake me. The word is not important, it is merely the clue to what is important: that which is called a "theorem" stems directly from the application of logic to a set of axioms that are unfalsifiable unless they are inconsistent, so barring the discovery that the axioms are inconsistent (which is also established with pure logic), no theorems are testable in the scientific sense. Yes or no? (And note that any similarity in the words "theory" and "theorem" are entirely incidental, they could be "alpha" and "omega" for all it would matter.)
To avoid getting off track here, I'll respond to that on the TBSP thread.But I really am interested for professional reasons why you think that the TBSP correlation coefficients (r2 scores) is a good example of when mathematics and assumptions don't gel. Because I don't see that at all. I'm just trying to understand what you are trying to say here. Your point went right over my head. Could you please be a little more explicit?
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The short answer in terms of what I perceive to be philosophy of science as you espouse it is "No". A longer answer follows.
I would certainly not recommend the sort of philosophy that I see as represented by "the disquotation theory of truth", but perhaps a philosophy of the sort that has in the past been reflected in the work of some real theoretical physicists and mathematicians, and perhaps that philosophy is more closely related to art than to philosophy as practiced by philosophers.
Please keep in mind that I am recently retired, and hence like philosophers have no need to be particularly useful, am under no pressure to publish anything, and certainly do not have to have an answer the MOND vs CDM question by Monday or next Monday or the Monday after that. Also, I ask your indulgence as what I am attempting to describe is difficult to verbalize, at least for me.
Dirac looked for beauty in his formulations of physics. So did Einstein, and so other top-ranked theoreticians. Wigner wrote of the unreasonable success of mathematics in the natural sciences in describing this beauty. Let me quote Feynman:
"To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once. " – Richard P. Feynman in The Character of Physical Law
Newton's mechanics is a beautiful theory. General relativity, which supplants Newton's theory is also beautiful. That beauty of general relativity arises from its underlying simplicity, which is reflected in the elegance of its formulation from a few fundamental physical principles and the astounding accuracy with which that elegance and simplicity translate to a description of nature.
We are now confronted with a problem in that galactic rotation rates seem to violate both Newton's and Einstein's theories of gravitation.
One proposal to address that problem is MOND. MOND is sometimes called an effective theory because it provides a model that can explain a phenomena but is not based on any new fundamental physical principle. One might call it ad hoc. I call it a curve fit. And curve fits are not beautiful. This one is hideous. I will be greatly disappointed, and I think Dirac, Einstein, Wigner and Feynman would share that disappointment if MOND were to emerge as a long-term solution to the dilemma posed by galactic rotation rates. As a short-term, ad hoc, purely empirical means of modeling galactic rotation rates for some specific objective it may have utility, I sincerely hope it is not the face of a fundamental law of physics.
Another proposal is CDM. As it stands CDM is not quantifiable. It is a place holder for something, what that something is remains a question, that occurs in sufficient abundance and is distributed in such a manner, that it provides the necessary gravity to explain galactic rotation without modification of general relativity or Newtonian mechanics. CDM may also be ad hoc and it has the potential to be every bit as ugly as MOND. But it also has the potential to provide a path to beauty.
I am no expert in particle physics and the standard model, but as an outsider the theory, while it seems to provide accurate predictions, also appears to be terribly ad hoc. The list of elementary particles is rather long, sufficiently long that Fermi once made a comment to the effect that if he could keep track of them he would be a botanist and not a physicist. If one believes that fundamental laws of nature will exhibit beauty, then one might hope that deeper understanding of particle physics might lead to an understanding that would be more simple in nature, and in that simplicity might also provide a theory that would be compatible with both general relativity and quantum mechanics. Perhaps CDM will be a result of such a theory. That would be beautiful. And perhaps the galactic rotation problem is a hint as to the nature of the revision to both particle physics and general relativity that is needed to effect a unification. Maybe the hint is that attempts to unify quantum theory and general relativity have failed because there is some flaw in general relativity on a very large scale that is wrong and that flaw prevents unification -- but I am way out of my depth on this one. Basically I am clueless as to what that hint might be. Ed Witten doesn't seem to know and I certainly don't.
There is a a third possibility of course. And that is that neither MOND nor CDM are the right approach. Perhaps one could look at MOND, translate it into a constraint on the a minimum rate of change in curvature in general relativity and relate it to some underlying physical principle rescuing MOND from the curse of ugliness through a relationship with geometry. This strikes me a difficult thing to do. I dunno.
Unfortunately this little bit of (horrors) philosophy on my part is probably of little use to a physicist who must produce tangible research and who is under pressure to publish. If anything it is perhaps reflective of the sort of musings that resulted in Einstein pursuing a lonely and unfruitful research path in his later years. Any real physicist even contemplating addressing issues on this level ought to at least have tenure, or be willing to live on nuts and sleep in a tent.
If there is tie between what I have said above and the original issue posed in this thread it is probably that in considering a physical theory and the issue of falsification of that theory one might look a bit beyond simple correlation with a small bit of experimental data. Einstein was convinced of the correctness of general relativity even before the initial experimental confirmation, stating before that confirmation that "If it is not proven, I pity the Good Lord, for the theory is correct." Such is the conviction that comes with a beautiful theory.
Order of Kilopi
Even axioms are testable against experience, I would say, along with Quine.
Please read at least read this one paper if for nothing else that you'll be able to claim in the future that you have at least read some of the primary literature in the philosophy of science: Two dogmas of empiricism. It's by Quine, first published in the Philosophical Review in 1951. It's got the whole text for free--no $29.50 necessary. It still is considered a landmark paper within analytic philosophy.
Here's a little teaser to get you interested:
It's right up your alley, actually!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. Physical objects are conceptually imported into the situation as convenient intermediaries -- not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. 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. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
That would be totally cool. I thank you!
Order of Kilopi
DrRocket, that was a very thoughtful post. If we were God, would we be able to make the universe beautifully and simply, without a bunch of ad hoc fixes? What if the literal hand of God was required to keep the clockwork wound up? Could the hand of God be an explanation for the galaxy rotation problem? After all, in a metaphysics -free science, the God hypothesis is as likely as any, is it not?
As for modified Newtonian dynamics (MOND), I see your point that it has not much of a physical basis apparently. Actually, if MOND is simply considered an empirical pattern, along the lines of Kepler's or Titius-Bode's, that is, if intended to be a mere description of what happens, the "cold" "dark" "matter" (CMD) wouldn't be inconsistent with MOND, but would actually be an explanation for the MOND pattern.
Then again, CMD sounds outrageously outlandish to my earthbound ears. Isn't there a mainstream explanation for galaxy rotation? Maybe the observations aren't what they seem???
But hey, what do I know? Today was the first day I've ever read about MOND or CMD (that I can recall), and so I am willing to kick back and listen. I shan't presume to tell any professionals from cosmologists to cosmetologists how to do their job.
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One approach to you first question is a coviction not only that God can make the universe beautifully and simply but in fact the He has done just that. The role of the scientist is to figure out just what those beautiful and simple rules are. One does not have to invoke God to do this, but simply be convinced by experience that the universe is governed by simple and beautiful rules. So far that conviction has proved to be accurate. Atheists and agnostics have pursued this path fruitfully.DrRocket, that was a very thoughtful post. If we were God, would we be able to make the universe beautifully and simply, without a bunch of ad hoc fixes? What if the literal hand of God was required to keep the clockwork wound up? Could the hand of God be an explanation for the galaxy rotation problem? After all, in a metaphysics -free science, the God hypothesis is as likely as any, is it not?
As for modified Newtonian dynamics (MOND), I see your point that it has not much of a physical basis apparently. Actually, if MOND is simply considered an empirical pattern, along the lines of Kepler's or Titius-Bode's, that is, if intended to be a mere description of what happens, the "cold" "dark" "matter" (CMD) wouldn't be inconsistent with MOND, but would actually be an explanation for the MOND pattern.
Then again, CMD sounds outrageously outlandish to my earthbound ears. Isn't there a mainstream explanation for galaxy rotation? Maybe the observations aren't what they seem???
But hey, what do I know? Today was the first day I've ever read about MOND or CMD (that I can recall), and so I am willing to kick back and listen. I shan't presume to tell any professionals from cosmologists to cosmetologists how to do their job.
If galactic rotation or anything else requires the acive intervention of God to keep the clockwork ticking then science is finished. Kaput. DOA. As soon as you invoke magic science goes out the window. At that point you can forget about confirmation or falsification of physical laws, because the dependence of nature on physical laws is itself an invlidated concept. We can then all hang out exclusively on the ATM threads. No thanks.
I would like to separate Kepler's laws from Titus-Bode's. Kepler's laws were derived from Tycho Brahe's observations and were iindeed not much beyond curve fits. But at the time there were no fundamental law's of mechanics. A slightly over-simplified history goes like this: Tycho Brahe made a whole catalog of observations, with no further analysis. His rather bright but underpaid assistant, Johannes Kepler came along and organized the data, fit some clever curves to it and formulated a set of ad hoc laws that accurately described planetary orbits. Along came Isaac Newton who admired Kepler's laws, but wondered what principle might explain them. Whether it was a falling apple or something else, he dreamed up the idea of gravitational attraction and tried to apply it to the planets. To do that he needed differential equations so along the way he invented calculus, and voila' from F=ma and little bit of freshman mathematics he reproduced Kepler's laws of planetary motion, but based physicall on no more than F=ma=GmM/r^2.
Actually I think CDM and MOND are mutually exclusive, at least in practice. MOND actually results in a modification of Newton's equations. CDM provides additional matter, properly distributed to account for galactic rotation with no modification of those equations. So if you add in CDM and then also use the MOND equations you will have overcorrected and again have a problem.
Maybe the galactic rotations are not what they seem. I dunno. If I were involved in research in that arena I would be checking the observations very carefully. The experimentalists are very clever at these things. But there are a lot of opportunities for mistakes. Personally I hate going through someone else's detailed experimental data looking for errors. I have had to do that in engineering applications (like rocket failures) but I am fundamentally bored silly doing it, although I recognize the need. That is why there are theorists and experimentalists. That is why I am grateful for the very existence of experimentalists.
Finially, if I were God I would certainly have made the universe beautiful and simple. And I would fix a couple of other things as well. I'm working on it, but don't hold your breath. If I get there you will notice the difference.
Order of Kilopi
This all hinges on what one means by "test". In science, a "test" means you confront a prediction with an observation. In philosophy, a "test" means you evaluate the ramifications of an axiom. The former is simply a quantification, the latter is a value judgement. The former is objective, the latter subjective. These are just a few of the very common ways that science and philosophy fundamentally differ.
Thus, if one is "testing axioms" against experience, in the sense of checking quantitative predictions, then one is doing empirical science, not math and not philosophy (what philosophical proposition resulted in a quantification of something what was later checked against experiment?). "Softer" forms of science are less quantitative, yet must preserve an aspect of making predictions that can actually be falsified, not simply "accepted" (no doubt there is a continuum of softer and softer forms of science until the distinction with philosophy gets more difficult to make-- I'm referring to the astronomy and physics mentioned on this thread). To the extent that philosophers are smart people applying quantitative tests of certain precisely expressible axioms against objective experience, they are acting as scientists, that's the definition of doing science. The pedigree doesn't matter, the work does. When a philosopher tallies numbers on their income tax forms, are they doing philosophy or math?
We are not labeling the individuals, we are deciding what constitutes science. If you can test it, repeatably and objectively, it's science-- that's the definition. Whether it's a physicist, a philosopher, or a two-year-old child. Normally that last is not considered a "scientist", but they can still be doing science, it's just not science that will be interesting to others.
Frankly, I feel I already have a better understanding of the philosophy of science then I have ever seen in a philosophy text. If I read it, it would be to critique it. There might be an idea in it that I both agree with and did not already know, but I doubt it. Let's take the part you quoted, for example:Please read at least read this one paper if for nothing else that you'll be able to claim in the future that you have at least read some of the primary literature in the philosophy of science:
Right away my "hackles" go up, because not only do I view that as an extremely limited and uninteresting angle on what science is, I think it is horrendous for a scientist to feel the need to "declare their ism" to preface their scientific perspective. A defining element of science is that it should be objective, so no "ism" needed, and a central lesson of relativity is that the laws of physics should be applicable equally by all observers. If nature gives us results that are unified beautifully by a principle that all observers see the same physics, why should observers feel that they need an "ism" to interpret what that physics is? Science is a way to organize and unify objectively repeatable observations, that's just its definition, and many possible "isms" could contribute to that process, there is no reason to take any one particularly seriously. "Isms" are taken seriously only when we extrapolate science in improper ways, when we attempt to describe what we personally choose to believe is the truth, but science has no need to include that piece, since that is not objective."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."
Again a problem-- no one should care what Quine has chosen to "believe", nor does any scientific paper require any expression of such beliefs. As I said before, when ten physicists say "an electron scattered off a proton", they can easily mean ten different things, and often do, depending on their specialty and their level of mathematical sophistication. Are they all "believing" different things, like Roman versus Greek gods?" Physical objects are conceptually imported into the situation as convenient intermediaries -- not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. 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."
No, belief simply has nothing to do with the usefulness of the concepts in that sentence, as everything in science hangs on hard evidence or it has no particular meaning or importance at all. The sentence is shorthand for that hard evidence, and different physicists might be considering a different body of evidence when they use that phrase. Fortunately, the "tower of Babel" problem is avoided in that the overlap of all the meanings retains the core usefulness of the concepts, and so an effective form of communication occurs, despite these different meanings.
That statement sounds pretty close to meaningless to me, as it lacks the crucial inclusion of a sufficiently precise definition of what is meant by "degree" versus "kind". I could easily offer plausible meanings of those words that make the sentence obviously true, or obviously false, so the real issue is, what is the meaning of those words that make that sentence interesting or useful in some way?"But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind."
Another meaninglessly vague remark. I'm sorry, but I can't think of any pair of entities that I could not apply that remark to if I strike the word "only", so apparently the meaning of the sentence is intended to be carried by the "only". But if one inserts a weak meaning for "only", it isn't peforming any function and we're back to the "motherhood remark", or if one inserts a strong meaning for "only", the sentence is obviously wrong-- if they were "only" cultural posits, how then could they have any value outside of what is cultural? How could they help us open a door or use a lever or fly to the Moon if they are allowed "only" to be cultural posits and nothing else, or if anything we do is to count as "cultural", then again what is the sentence actually saying that isn't obvious? So what does he think the word "only" means here? It's just spectacularly vague to the point of meaninglessness."Both sorts of entities enter our conception only as cultural posits."
OK, one single remark that is actually true. But it is obviously true, I learn nothing from it. To me, that sentence says nothing other than the definition of science, and I would synonymously rephrase it as "science invents concepts and labels, not to make them real, but simply as devices for organizing and unifying the results of objectively repeatable observations". Yup, I know that, I'm a scientist. Is there anything else being said in that statement that I missed?"The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience. "
I can't because the thread is closed. I'll just mention that whenever I see someone claim a statistical correlation like 0.99, and I see data that is quite frankly ratty and picked over, I know that a rat is afoot. First of all, the TBSP in our solar system requires a deviation from logarithmic or it completely fails for the planets closer to the Sun than Mars. What then is the justification for the first 3 planets completely failing to follow a logarithmic distribution? How does one accomodate such "freedom of selection" when making a correlation coefficient? Then we have Ceres, which is included because it fits, even though its mass is a tiny fraction of the mass that would have been in the original asteroid belt (much of that belt has been ejected by interactions, but Ceres' mass should not have changed appreciably). It would make more sense to group all the asteroid belt together and find an average semi-major axis for the whole shebang. Finally, Neptune fails completely, yet sometimes people include Pluto. If your coefficient does that it's obviously improper, because why should a huge planet like Neptune be left out and a tiny planet like Pluto included? I don't know exactly what choices you had to make to get that coefficient, but I'll wager you did not simply line up the ten most massive objects in the solar system and test their logarithmic spacing.That would be totally cool. I thank you!
Last edited by Ken G; 2008-Jul-28 at 07:54 AM.
Order of Kilopi
I call evaluating ramifications of axioms "mathematics"--not philosophy. BTW, since your whole argument for separating philosophy and science is entirely definitional, we need to know your definition of philosophy (I actually pretty much agree with your definition of science.) The reason we keep talking past each other, I suspect, is that your view of philosophy is a strawman caricature of the actual discipline. (And by "philosophy", I'm referring to the respectable Anglo-American analytic brand, and not the continental, deconstructionist, postmodern, version.)
HAHA! That's very funny, because I was just about to suggest with all this MOND and CMD and DE and accelerating universes stuff going on that astronomy and astrophysics are about to supplant economics and ecology as the new "dismal" sciences!
Even cats can do science the way you describe it--I watch the new kitten I got develop his own little ontology, and he's constantly testing things, e.g., repeatedly poking a bowl of water with his little paw. So he's doing "science". But we don't call 2-year-olds and cats scientists. The cat is still a cat. So a philosopher doing science would still be a philosopher because he or she would be conducting the science for their own philosophical purposes.
[MOST IMPORTANT]Thus to answer your question "(what philosophical proposition resulted in a quantification of something what was later checked against experiment?)" I can give you an example from my personal experience. I once constructed a quantitative model of Jupiter's Great Red Spot not because I have burning interest in the GRS (although it is very cool) and not because my primary goal was to make a contribution to planetary science (although if I could that would be great); no, the primary reason for me to do the "science" as you say, was to empirically test a pet philosophy of science theory of mine: that biological modes of analysis can be successfully extended to "mere" physical systems. So is what I did science or philosophy or neither, or perhaps a little bit of both?[/MOST IMPORTANT]
But your sample size of philosophy texts is apparently quite small. Not very scientific of you, my friend!
You're starting to worry me: how is Quine's "I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience." different in any way from the definition of science you espouse?There might be an idea in it that I both agree with and did not already know, but I doubt it. Let's take the part you quoted, for example:
Right away my "hackles" go up,
Don't be so paranoid--being an empiricist is a good thing and something to be encouraged--especially among scientists!
When Quine said he believes in the posits of science, I think he's just expressing the fact that he's a naturalist, so as to reassure scientists that he's not out to deconstruct the scientific project.
That's why conceptual analysis--a traditionally philosophical task--is so important.
Dude, you've got to read the paper! That's what the whole paper tries to explain!That statement sounds pretty close to meaningless to me, as it lacks the crucial inclusion of a sufficiently precise definition of what is meant by "degree" versus "kind".
No, when you say things like that, you are being a philosopher of science.
There's a new thread that discusses a recent Russian paper from the ArXiv that attempts to debunk Poveda & Lara's (2008) analysis of the apparent Titius-Bode-style spacing at 55 Cancri.
For some reason, no one seems to want to take Ivan's side and defend him, though. Maybe you can! (heh, heh, heh. . . .)
First of all, the 0.997 r-squared was for 55 Cancri--not the solar system. But my best fit for the Solar System is 0.15 + 0.14 * 1.8n--a nice simple formula with that gives an r-squared of 0.996. Not bad. The only planet I leave out is Pluto, because of the a priori reason that Pluto's dynamically locked in an orbital resonance with Neptune, and therefore does not constitute an independent sample. (I also just used the Ceres orbit--others have used averages, and the average is quite close to Ceres, so it doesn't affect the analysis). The residual of Neptune is only about 1 AU--3.5%. So we have this measurable pattern in two solar systems now with seemingly high correlation coefficients. That is, the TBSP patterns are apparently not "falsified" by statistics--or so I would think. The question is what to do with the empirical pattern. Should we allow the TBSP to constrain planetary formation theory or not? Because if we do, then any theory that can not reproduce an exponential spacing pattern would be falsified by the TBSP itself, would it not? So my point is that answers to these kinds of questions are kind of subjective--and the way forward is not at all obviously clear. But I guess that's why you guys get the big bucks!
But if we want to discuss this more (I would actually be interested in your take on the Russian paper), we had probably better take it over there. The philosophy versus science debate has hijacked this thread bad enough. We're going to get ourselves banned if we're not careful!
Last edited by Warren Platts; 2008-Jul-28 at 09:31 PM. Reason: insert 'and' between 'ecology' and 'economics'
Order of Kilopi
No, it's not. This can probably even be checked in Wikipedia. And yes, it is a theorem, not a "theorem".
Established Member
I don't much care what you checked out in Wikipedia. Conditional probability as defined in a rigorous measure-theoretic treatment essentially incorporates Bayes "theorem" in the definition. Take a look at, for instance, Probability Theory by Loeve to see what I mean. You see it treated in elementary texts as a theorem largely because elementary texts do not present probability in a rigorous (i.e. measure-theoretic) manner. But once Kolmogorov put probability in a rigorous setting, Bayes "theorem" became clear as simply the definition of what is meant by conditional probability.
Order of Kilopi
No, that is total nonsense. Bayes' Theorem is provable from the definition of conditional probability in elementary probability theory (the Wikipedia article has the proof).
You may be thinking of some extension of it for infinite probability spaces. But since the real world that each of us actually lives in is finite, that is beside the point.
Established Member
Not at all. What I am thinking of is this. A priori, the notion of conditional probability is simply intuitive. It requires a rigorous definition to be used in calculations. The definition of conditional probability is siimply P(AlB ) = P(AB)/P(B), assuming that P(B) is not 0. This definition requires a bit of measure theory to make precise. But the definition is what is called Bayes theorem in many treatments. Wikipedia merely calls Bayes theorem the relationship between P(AlB) and P(BlA): P(AlB)=P(BlA)*P(A)/P(B). This so simple that it does not deserve to be called a theorem, and often is not. Let me show just how simple it is:
P(AlB)=[P(AB)/P(B)][P(A)/P(A)] = [P(AB)/P(A)][P(A)/P(B)]=P(BlA)[P(A)/P(B)].
All of the work and all of the real content are in the definition.
This has nothing to do with the nature of the probability space.
Order of Kilopi
Well, technically, isn't '2 + 2 = 4' a theorem? I thought that any well-formed sentence within arithmetic that can definitively be proved to be consistent with the axioms counts as a theorem.
ETA: Because otherwise, wouldn't we have to call Bayes' theorem "Bayes' axiom" instead? I'm sure we both wouldn't want that!
Established Member
\
Very technically, yes, but in mathematics the word "theorem" is normally reserved for important results. 2+2=4 is theorem only because in the construction of the number systems 4 is defined as 3+1. But one can go through the entire construction, starting from the natural numbers and ending up with the complex numbers and not find a named theorem.
To name a trivial result as a theorem with someone's name attached is tantamount to an insult in many quarters. Or a joke.
What Wikipedia calls Bayes Theorem is so trivial that it fits in the category of a joke (I don't think anyone would want to insult Bayes). Loeve defines conditional probability and derives "Bayes Theorem" in the general form that applies to n events A1,...,An in about 3 lines. Feller doesn't even name it. And Billingsley calls it "Bayes formula" and leaves the derivation, for the general n-event, case as an elementary exercise. It is perhaps handy to have a name for the general formula and "Bayes Theorem" or "Bayes formula" serves that purpose, but it does not have the necessary importance to be what a mathematician would call a theorem.
One result of the triviality of this formula is that mathematicians use the term Bayes Theorem, if at all, very loosely. I was brought up with the terminology being identical to the definition of conditional probability. But this looseness does not matter because the various forms are related so easily that any mathematician can go from one to another quickly, usually without need even for paper and pencil.
Added it edit: There is probably also some history involved, that I don't know about. Conditional probabilities and "Bayes Theorem" are older than the modern measure-theoretic formulation of probability, which is due to Kolmogorov in the 1930's.
Last edited by DrRocket; 2008-Jul-28 at 07:49 PM. Reason: Add clarity
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Well, Bayes' Theorem most definitely is important!
And, as you put it, it is a "result". In other words, a logical consequence of the definition P(AlB) = P(AB)/P(B) and of Kolmogorov's axioms of probability. It's not part of the definition of conditional probability.
That its proof is simple is irrelevant. Lots of important mathematical results have simple proofs.
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I agree that a clear meaning for the term "philosophy" is required, but I require your definition of that term as much as you require mine. To me, the crucial difference between science and philosophy, and why it is so crucial to distinguish them, is that science manifestly involves an objective interaction with nature, while philosophy is manifestly subjective. Of course there is no such thing as either of those notions, yet they are useful models, and what I mean by them is that "objectivity" seeks to separate the subject from the object and focus the attention on the object, as if there was no subject involved. Subjectivity, on the other hand, is primarily interested in the subject, and how the subject reaches the conclusions it reaches and what kinds of interactions with the environment are possible. Science intentionally "looks past" the subject, simply because not doing so bogs it down unbearably, whereas philosophy cannot affort that luxury because it seeks to understand the subject, moreso than the object, of the exercise.
Now, of course we cannot really be "objective", we are subjects. But, the pretense of objectivity is not a flight of fancy, it is a vastly useful and effective way to study the universe in which we live. But it wasn't until we got our own minds "out of the way" and split science from natural philosophy that we realized the true progress possible when one simply trusts the voice of nature, as translated into the concepts of our minds, rather than expecting those concepts to intuit or reason toward nature.
If there is one philosopher I generally tend to agree with, it is Kant, and his "Critique of Pure Reason" may be saying much of the same things as this. Note I tend to form my views in advance and then look for confirmation in things Kant was saying, as it's rather hard to read him in advance and I find it easier to just look at the situation myself. I don't mean to demean the efforts of philosophers, nor can I trace how my own thinking evolved and what possible influences, direct and indirect, philosophers may have had. I merely argue that science works better when clearly distinguished and separated from philosophy, and that conclusion may be the best thing philosophy has ever given science.
But that reveals a misunderstanding about the difference between "hard" and "soft" science. Some people think it has to do with the certainty of the conclusions-- it has nothing to do with that. Both forms have tentative and solid conclusions. What the difference actually has to do with is the mode of testing, pure and simple, and how quantitative it can be. A "hard" theory makes a prediction in the form of a quantity, and then goes and tests it, updating whatever quantitative free parameters exist in the theory. That's the difference. CDM and MOND theories are certainly in that category, even if highly tentative and rather weakly constrained at the moment.HAHA! That's very funny, because I was just about to suggest with all this MOND and CMD and DE and accelerating universes stuff going on that astronomy and astrophysics are about to supplant economics ecology as the new "dismal" sciences!
Of course cats can do science, we just can't tell how well because we don't really know what is going on in that little mind. Do you think there is something "magic" about human intelligence? If so, could cavemen do it, or did science appear with civilization? Can a severely retarded human do science? There is obviously no "line in the sand" you can draw and say that "science starts here".Even cats can do science the way you describe it--I watch the new kitten I got develop his own little ontology, and he's constantly testing things, e.g., repeatedly poking a bowl of water with his little paw.
I already said that myself, it poses no challenges to my position. A professional scientist is the same difference from everyday science as a professional tennis player is from me playing with my friends. Would you say I am not playing tennis, just because I am "not a tennis player"?But we don't call 2-year-olds and cats scientists.No, science is defined by the scientific method, and if it is being followed, it is science, and if it isn't, it's not. When Roger Federer is throwing a frisbee, is he really playing tennis?So a philosopher doing science would still be a philosopher because he or she would be conducting the science for their own philosophical purposes.
But that is not what I asked you to provide-- what you describe is using a philosophical principle to motivate you to try a particular model. It matters not to science what inspiration people use to try various models, I pointed out that even a good poem might inspire some model someday, does that mean it does not make sense to distinguish science from poetry? The inspiration is a subjective issue, science is concerned with the objective result. It's just like how musing about Mach influenced Einstein, an influence I not only didn't deny, I brought it up.I once constructed a quantitative model of Jupiter's Great Red Spot not because I have burning interest in the GRS (although it is very cool) and not because my primary goal was to make a contribution to planetary science (although if I could that would be great); no, the primary reason for me to do the "science" as you say, was to empirically test a pet philosophy of science theory of mine: that biological modes of analysis can be successfully extended to "mere" physical systems.
Thus your example merely underscores the subjective/objective dichotomy I made earlier-- in what you describe, I have no trouble distinguishing at what points you were engaging in philosophy, and at what points you were engaging in science, and I also see how terribly confused the whole effort would have become if we could not distinguish those pieces.I am certainly no expert in philosophy, but I am also no expert in religion-- yet I have little trouble distinguishing science from that either.But your sample size of philosophy texts is apparently quite small. Not very scientific of you, my friend!
It only misses a large fraction of what science is all about. For example, it would apply equally well to what I call "google science", which is, simply categorizing and storing information on all experiments that have ever been done, and interpolating to predict any new experiment. Hardly good science, that, but it fits Quine's idea of what science is to a tee.You're starting to worry me: how is Quine's "I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience." different in any way from the definition of science you espouse?
No-- there is nothing gained from being an "ist" of any kind in science, other than "one who conforms to the scientific method". You can call that its own "ism", but it is simply a definition.Don't be so paranoid--being an empiricist is a good thing and something to be encouraged--especially among scientists!
I agree, but I think he also exposes a lack of understanding of what science isn't-- a "belief machine". One that many scientists share, I will grant you.When Quine said he believes in the posits of science, I think he's just expressing the fact that he's a naturalist, so as to reassure scientists that he's not out to deconstruct the scientific project.
Then that is the only thing of value he is saying, and he should save all this other stuff and just get to the point. If he just said "here's a meaning of kind, and a meaning of degree, and here's how it informs us about scientific objects versus gods", then I could read a few paragraphs of description without having to suspend disbelief the whole time.Dude, you've got to read the paper! That's what the whole paper tries to explain!
I am often a philosopher of science. I just separate it from science. If knowing what science is all about is philosophy, then it is important for science. But it isn't science.No, when you say things like that, you are being a philosopher of science.
But the law obviously fails utterly for Neptune, and what is that 0.15 doing in there? That's not a logarithmic law, it's pure numerology. I think this says nothing but that there is some mechanism, among the many other ones going on, that makes gas giants want to be about twice as far as the prior one. It's way over-interpreted by the correlation coefficient analysis.But my best fit for the Solar System is 0.15 + 0.14 * 1.8n--a nice simple formula with that gives an r-squared of 0.996. Not bad.
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Quote:
But my best fit for the Solar System is 0.15 + 0.14 * 1.8n--a nice simple formula with that gives an r-squared of 0.996. Not bad.I think there is another point to be made here as well. A simple curve fit is poor science no matter what the r-squared might be.But the law obviously fails utterly for Neptune, and what is that 0.15 doing in there? That's not a logarithmic law, it's pure numerology. I think this says nothing but that there is some mechanism, among the many other ones going on, that makes gas giants want to be about twice as far as the prior one. It's way over-interpreted by the correlation coefficient analysis
The objective of a scientific theory is to provide an exact description of a physical phenomena. Let me talk for the moment only about classical theories, for the sake of clarity. We know that there are always measurement errors and we know that our theories are only very good approximations. Nevertheless, we expect that a good scientific theory will explain the relevant phenomena sufficiently well that any and all observations will agree with it within the error limits for the technology used to make the measurements. When it does not, we look for previously unrecognized errors in the measurement or we look for a new theory. The error limits are specific to the experiment in question, and when evaluating the experiment itself statistics and r-values are useful. But if you have solid data which you believe to be "true" to a very high level of accuracy. Then an r-squared of 0.9 or 0.99 or 0.999 or whatever is not good enough agreement between that data and the predictions of a theory. Agreement is close enough when all predictions of a theory agree with all experimental data within the expected error limits for each and every experiment. If you don't have that kind of agreement you start re-evaluating the experiments or re-formulating the theory. In terms of the original question posed in this thread, if your theory fails to agree with experiment within the expected errors in the experiment itself, then you have falsified the theory, and at least indicated the domain in which that theory can be applied as a useful approximation.
Everything that I have just said also applies to quantum theories, with the added wrinkle that in those theories the actual prediction is a probability distribution. That makes a discussion of the role of statistics more complicated than is the case with classical theories, but the basic idea is the same.
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My definition of 'philosophy' is the original Greek definition: "love of wisdom".
Absolutely not!But that is not what I asked you to provide-- what you describe is using a philosophical principle to motivate you to try a particular model.I can give you an example from my personal experience. I once constructed a quantitative model of Jupiter's Great Red Spot not because I have burning interest in the GRS (although it is very cool) and not because my primary goal was to make a contribution to planetary science (although if I could that would be great); no, the primary reason for me to do the "science" as you say, was to empirically test a pet philosophy of science theory of mine: that biological modes of analysis can be successfully extended to "mere" physical systems. So is what I did science or philosophy or neither, or perhaps a little bit of both?You asked whether a philosophical proposition "ever resulted in" a quantitative prediction. I said I "constructed a quantitative model" in order to "empirically test a pet philosophy of science theory". But you say what happened is that the pet philosophy of science theory "motivated" trying a "model", as if "motivating" is different from "resulted in" or "constructed in order to".
Apparently, you meant that as a rhetorical question, never figuring that I actually would have an answer to that.
So you want a risky prediction that can be verified by experiment??? OK, how about this:
Whatever it is that causes the red coloring of the GRS has a density between 1.0 gm cm-3 and 0.7 gm cm-3.
Sorry, but I can't check on this myself--I don't have a fully stocked chemistry lab in my spare bedroom--perhaps you do?
For you to intimate that that concrete recommendations on how science might be done on the basis of rational consideration of the philosophy of science is on the same level as a guy smoking opium and staring at a fire and imagining snakes eating their own tails while listening to classical music and reading poetry is entirely unfair.
My hypothesis was not the result of inspiration--it was the result of much perspiration--years of study that finally came together. It might turn out to be nothing--it might turn out to be true. But whatever, it was a fully self-conscious, rational thought process from beginning to end. It was science in the service of philosophy--and it was philosophy in the service of science! It wasn't "inspiration" as when one smokes a joint, reads some poetry, listens to some classical music, takes a little LSD, or any other way you can think of to belittle, trivialize, demean my hard work! And you've got the nerve to accuse me of sophistry. . . .
The fact is, your argument is based on nothing but your own idiosyncratic, personal "definitions" that you have in your own mind. You demonstrate zilcho willingness to look beyond your own, dusty library--if you have one at all. The fact is there is nothing that will ever happen, ever will be written, ever will be seen that will cause you to give a single inch. Is there? You want to talk about falsification: what would falsify your view that science and philosophy are separate magisteria?
Never mind. . . .
You've asked for evidence that would challenge your position, and when it is presented, you ignore it, dodge it, or twist it.
Last edited by Warren Platts; 2008-Jul-29 at 01:35 AM. Reason: sp.
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So, just how many angels can dance on the head of a pin?
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Define the size of an angel and I'll tell you.So, just how many angels can dance on the head of a pin?
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Obviously begs the question: how do you ascertain wisdom? You can do better than that, you are one, right?
Then we are in complete agreement that cats can do science, albeit rudimentary. So why did you bring it up?Absolutely not!
But the "in order" does not say that the philosophy was what constructed that model. The philosophy just said you might want to try constructing such a model-- everything you did when you actually constructed it was straight science, no philosophy there. What philosophical writings did you use when you constructed the model of the GRS (not when you decided you would try to construct the model-- I covered the issue of "inspiration" several times above). What philosophy does the GRS satisfy, the one that says models that work in one area might also work in another? Scientists with zero philosophical training do that all the time.You asked whether a philosophical proposition "ever resulted in" a quantitative prediction. I said I "constructed a quantitative model" in order to "empirically test a pet philosophy of science theory".
Yeah, as if deciding that we needed a new relativity is different from sitting down and constructing it. Yes, it is different, totally different-- it was the difference between Einstein and a hundred of his contemporaries.But you say what happened is that the pet philosophy of science theory "motivated" trying a "model", as if "motivating" is different from "resulted in" or "constructed in order to".
On the contrary, your answer is just what I would have expected, and actually proves the point I'm making about the difference between how to make a model, and why to make a model (the former being judged as an objective endeavor, the former being the subjective undertaking).Apparently, you meant that as a rhetorical question, never figuring that I actually would have an answer to that.
No, I see that aspect as orthogonal to what matters here.Next you'll say a model is not the same as a prediction.A statement with zero philosophical content, it's just pure science. If you doubt that, please tell me which philosopher would be troubled if you are right or wrong. Who is going to think their philosophy must be off the mark depending on how your assertion tests out?My model predicts that the GRS reaches down to the PPT, in contrast to the standard "pancake" model.
Pure science. I see no relevance at all to the discussion at hand.Whatever it is that causes the red coloring of the GRS has a density between 1.0 gm cm-3 and 0.7 gm cm-3.
You are describing science here. At what point were you following the scientific method, and at what point were you following the philosophic method? Have you even defined the philosophic method? If not, what do you imagine the word "philosophy" can mean, other than the ultra-vague and historical "love of wisdom"?My hypothesis was not the result of inspiration--it was the result of much perspiration--years of study that finally came together.
No, it was just science when it was science, and it was just philosophy when it was philosophy. At no point in that process were you ever doing both at once, it's relatively easy to make the delineation simply by referring to their definitions (at least the ones I've offered-- your definition isn't useful for anything as it applies to a priest as easily as to a philosopher).It was science in the service of philosophy--and it was philosophy in the service of science!
You have entered your own head at this point, I see zero projection of what you are talking about here and anything I said or meant.It wasn't "inspiration" as when one smokes a joint, reads some poetry, listens to some classical music, takes a little LSD, or any other way you can think of to belittle, trivialize, demean my hard work!
That is "argument by objecting to definitions". Too convenient-- definitions are what make our statements precise. If you object to someone else's, but offer no useful ones yourself, you are simply engaging in imprecise use of language. Shouldn't a philosopher know better than that?The fact is, your argument is based on nothing but your own idiosyncratic, personal "definitions" that you have in your own mind.
On the contrary, there is just one: an effective argument with clearly defined terms and an identifiable logical flow. To that, I'd give a mile.The fact is there is nothing that will ever happen, ever will be written, ever will be seen that will cause you to give a single inch.
That statement is not a statement by science, it is a metaphysical statement about science. As such, it need not be falsifiable in the sense of scientific experiment, instead its value rests on its logical emergence from its own definitions. It is the philosophy of science that tells us science is not philosophy, and there is no contradiction there, it's perfectly logical. What's more, it's true.You want to talk about falsification: what would falsify your view that science and philosophy are separate magisteria?
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Agh! The vultures are circling closer!So, just how many angels can dance on the head of a pin?
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I'm begging questions? That's a good one Ken--especially coming from you. . . .
My one sentence definition of philosophy is that it is the systematic analysis of all forms of human intellectual endeavor-including empirical experience. This agrees with the relevant standard dictionary definitions:
1. the rational investigation of the truths and principles of being, knowledge, or conduct.
4. the critical study of the basic principles and concepts of a particular branch of knowledge, esp. with a view to improving or reconstituting them: the philosophy of science.
The fact is, philosophy and philosophers are very much concerned with empirical experience. They also organize observations. Call it doing science if you want. But it's also doing philosophy as well--a point that's certainly not ruled out by my definition nor of Quine himself:
So there you have it: philosophy and science are not qualitatively different activities. They grade into one another. There are differences between science and philosophy, but the difference is a matter of emphasis.For Quine, . . . philosophy was no longer a tribunal outside and above science. 'Unlike Descartes,' Quine wrote, 'we own and use our beliefs of the moment…until by what is vaguely called scientific method we change them here and there for the better.' Critics thought Quine abandoned philosophy for science altogether. Quine said otherwise. True, there was no longer the grand dichotomy between philosophy and science, but there were important differences of degree (as with the more speculative reach of philosophy and greater breadth of its categories).
Clearly, because you maintain a hard and fast qualitative distinction between science and philosophy, as well as your vague references to DesCartes' "cogito ergo sum" and Kant, your philosophy is obviously stuck in the outmoded "first philosophy" of the 18th century that was demolished by 20th century analytic philosophy. That's why we keep talking past each other. You're not aware--on purpose, apparently--of anything that's happened in philosophy for the last hundred years! I don't blame you for wanting to critique Quine's philosophy of science--philosophical encroachment of "your" scientific turf must really stick in your craw. But you would do a better job of critiquing philosophy if you became acquainted with the real thing, instead of an antiquated strawman version.
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So to return to the thread topic, just as it would behoove someone with a batch of data to be analyzed to consult with a statistician, when one is confronted by the dilemma of two rival theories that cannot be decided on the basis of the available empirical evidence, then it would behoove that someone to consult the philosophy of science to see what it says.
And philosophy of science clearly says to accept (provisionally of course) the theory whose rejection would cause the most damage to the web of beliefs that constitutes one's overall theory of the world. That is, the choice should be made on the basis that will result in the fewest revisions of truth values elsewhere in the belief system.
Thus, to return to the neutrino example, to reject the conservation of energy principle would cause major damage everywhere; whereas rejecting the notion that the list of fundamental particles was complete, hardly anything has to be changed at all.
As for MOND versus CMD, the choice is more difficult because both theories are rather outlandish and require major rethinking either of the laws of physics or a radical revision of what we thought matter was like. It would be best if we could reject both of them IMHO! Of the two, my initial guess as an outsider would be to reject CMD since rejecting CMD would leave the universe of galaxies as we once knew them more or less untouched. MOND, on the other hand, though seemingly ad hoc and mathematically inelegant, it is at least mostly harmless, in that it only affects situations where accelerations are immeasurably small. But of course that is just the speculative first guess of an ignorant outsider.
In general, one should not throw one's weight around without reading and understanding the relevant literature first. . . .
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