Posted on 12/11/2002 6:28:08 AM PST by A2J
This is conceptually incorrect regarding a mathematical "theory". "Proving" a mathematical theory simply establishes that it is consistent with the assumptions of the established framework of discussion; it says nothing about whether or not it is true in any sense of the word.
Right, but the real world is curved and higher-dimensional. Of course, Euclid works as a splendid approximation, and hence is useful, but if you're talking in absolute physical terms about "true" vs. "false"...
Now, who's going to be the one to bring up the issue of provability? :-)
It doesn't even establish that with certainty. Several famous examples exist. The four-color theorem was proved for a while, and then went back to being unproved. "Principia Mathematica" was accepted for about 50 years before an industrious grad student found a flaw in the proof.
Anything humans, being fallable finite entities, have to turn a crank on to produce results, such as proofs in formal systems, is subject to recall.
Unless you can specify the exact chemical and morphological mechanisms by which life came to be, you do not have a believeable warrant to calculate the odds against it.
My interloctor made a statement about "universal gravity", not pragmatic local gravity. Here would be an equivalent question: Would you give your child an aligator fry to raise on the theory that Darwin was full of beans, and aligators are just as likely to re-produce lambs as gators?
I prefer "least inadequate".
Yes, that too is a factor to consider.
Ah, the conspiracy theory of book authorship. Of course, what was I thinking?
Attacking the man with vague accusations which of course cannot be refuted because they are so vague.
Yea, you hope anyway. Miller wrote an entire book about Behe, Dembski, and Johnson: "Finding Darwin's God". And it is far from vague, it is referenced up to its gills, and you will find the relevant references as to when and where, exactly, Behe's predictions were contradicted BEFORE Behe published.
Methinks he cites Miller, methinks reciting arguments in your own words doesn't not constitute plagerism, and methinks this is just a churlish emitting of wind.
Perhaps, but not by scientists, who are almost universally careful to point out that all scientific theories are held tentatively, whenever asked in a public arena.
Geordano Bruno didn't fare quite so well. But, then, he wasn't buds with the Pope, either.
You are right that I do not accept common descent as a "fact". It's a hypothesis which fits the facts. Any competing hypothesis would have to fit the same facts. But it wouldn't have to "explain" common descent because that's a hypothesis and you have no way of knowing that it's true.
Is your having a great-great-great-great-great grandfather--several of them, probably--a hypothesis as well?
Like I said before, yes. A very very believable one. In fact I'll grant that statements such as "I had a great^5 grandfather" come as close to scientific facts as it gets.
If it is, what's the use of insisting upon such ridiculous legalisms?
In short: Referring to common descent as a hypothesis rather than a "fact" allows you to make true statements rather than false ones.
The real difference between a scientific theory and a hypothesis (or a conjecture or a fairy tale) is that a scientific theory explains observation in some recognizably systematic, insightful, and rational way.
I'll agree with that. In precisely this sense, "the theory of evolution" is a theory.
JEEZ WHIZ MAN. What the HELL are you even arguing for? All I'm saying is that the theory of evolution is a theory!
(That's why it's called "the theory of evolution", capisce?)
No scientific theory, Darwin's or Gould's or anyone else's, of the diversity of life will get away with ignoring the evidence of [..]
True enough. You don't even have to complete the sentence. No scientific theory may ignore evidence.
the clear result of common descent.
A plausible hypothesis, I'll grant.
I may have the wrong term, it's been a while. But it has to do with the (mathematical) definition of a "fluid" for the purposes of fluid mechanics (which is probably the relevant mathematical "theory" here, not just "PDEs" as I had said.)
Scientist-type people want to model the behavior of (say) water. Water is a collection of a humongous number of particles (molecules). To simplify their predictions scientists want to use physical laws (i.e. Newton's F=ma law, conservation of mass..) to derive some kind of equations, which they can then solve. The mathematical solutions will then predict the behavior of quantities such as the "density" or "velocity" of the water, at various physical points.
Let's stick with "density". How do you go about defining the "density" of water at such-and-such location in the Pacific Ocean? You take a big box, say ten miles on a side; you count the particles in it; and divide by the volume of the box. Too coarse, too inaccurate? Fine, make the box smaller, a mile on a side. Or a meter. It seems like you're getting somewhere. The smaller the box, the better; your "density" measurement seems to settle on a definite number; what's better, you can get usable "density" measurements at a higher and higher number of points which are closer and closer together.
The problem is, this can't continue forever, because water isn't actually a (let's call it) "continuum". It's just particles. So after some point, your box is so small that it contains only one molecule of water (if the box happens to be centered where a water molecule is), or zero molecules (more likely). One or the other. After this point your "density" measurement becomes junk; at each location of the ocean the "density" is either zero or infinite, it's just a bunch of delta function spikes. This makes it hard to write down equations for it and predict things.
So what is done is, some kind of assumption is (necessarily) made that it's valid to study an abstract "fluid" which has smoothly-varying properties such as density, velocity, etc at every point of space. This is not actually true of actual fluids in the real world, but it is assumed that it's valid to neglect the fluctuations etc at the molecular level. So, you imagine measuring "density" etc with boxes not vanishingly small, but which are "not too small" - in some intermediate range, and endowing a (mathematical) "fluid" with those properties. Then you can write down all the PDEs you wish, but you have to hope that the "continuum assumption" you've made in the process doesn't make your model fatally inaccurate, when you try to connect your predictions back to the real world. This is a thing that has to be checked, and sometimes the "continuum" assumption is not valid.
I probably haven't explained very well but that's about the best I can do for a 400-post thread ;-)
I can't tell whether you honestly don't understand what I'm saying, or are just being intentionally obtuse for the purposes of prolonging the argument.
In brief: Scientific theories contain statements which may be falsified upon further data; mathematical "theories" consist of nothing but true statements (theorems). Scientific theories can be disproved and mathematical theories can't. That's the difference.
After making me frame this difference in plain English for the third or fourth time, for you to protest that you "don't see the difference" is to say nothing more and nothing less that you don't understand English. The main difference for this discussion consists of the second-to-last sentence of the preceding paragraph; if you still "don't see the difference" at this point all I can ask you to do is to read that sentence again until you do, or get tired.
To be sure, I understand (and already agreed to) the very minor point that if you view things abstractly enough then "mathematical theories" and "scientific theories" are similar, in the sense that they are both "theories". (Duh.) But this only goes so far. There are still those pesky adjectives "mathematical" and "scientific" in front of the two terms, and you can't just ignore them. Adjectives have a funny way of modifying the nouns they precede, and this can lead to precision and differentiation. It's like you don't understand this, or are pretending not to, for some reason.
It is precisely as if I was posting on a thread about ice cream cones. Post after post discusses this type of cone vs. that type of cone - some prefer waffle, others prefer the pointed kind, whatever. In one post I say "boy oh boy, yessirree, I sure do love all these kinds of cones."
Then Doctor Stochastic chimes in, "Oh yeah? What about pine cones?" This is a superficially clever type of comment, but only for a moment, and in particular only from seven-year-olds. All that is required to say is, "that's not the kind of 'cones' we've been talking about. Sorry." And that's what I did say, come to think of it.
The problem is that now, you, "Physicist", have valiantly rushed to Doctor Stochastic's aid, for some reason. "Are too! They're both cones! I don't see the difference!"
Now look, I guess I agree that viewed abstractly enough, both ice cream cones and pine cones are types of cones (very roughly speaking), and so, there ya go. (One comes to this dazzling conclusion by ignoring the modifiers "ice cream" and "pine", just as you've ignored the modifiers "mathematical" and "scientific".) But you'd never say "So therefore I don't see the difference between ice cream cones and pine cones!" And I'm also pretty sure you wouldn't eat a pine cone.
Now, I've stated several times that "mathematical theories" and "scientific theories" differ in that the former may never be disproven, placing them in stark contrast to the latter. The former make predictions about the real world, and the latter don't. And you're saying you "don't see" the difference.
I think the only thing left to decide is whether you do this out of denseness or just to be a nuisance.
A mathematician considers a theory "right" if only it is self-consistent. By contrast, "right" or "wrong" for a scientific theory also addresses the question of whether or not it applies to the real world.
Let me get this straight, you're trying to help me prove my point right? After all here you are detailing a way in which "mathematical theories" and "scientific theories" differ (standards of "rightness"). So why all that disingenuous crap about pretending not to understand the difference?
But I can also apply the same standards to mathematical theorems: an experimental test of Euclid's theorems shows that they don't apply to real spaces as well as Riemann's do.
"Don't apply to real spaces" means they are false (or at least inadequate) as "scientific theories" meant to describe the real world.
In the meantime, the mathematical theorems, or "the theory of Euclidean geometry" if you will, are just as true as ever - and will ever remain thus.
You're still helping me illustrate my point.
To me, Riemann is "right" where Euclid is "wrong".
As scientific theories, perhaps you are right. As mathematical theories, of course you are wrong.
This is an illustration of precisely my point, which was that scientific theories are different from mathematical theories.
So you see, it isn't that the word "theory" is used differently in mathematics and physics, but that the standards of "right" and "wrong" are different.
Sigh. So my earlier comments that "scientific theories can be proven wrong, mathematical theories can't" is wrong in your eyes, because, see, what I'm supposed to do is to switch the definition of "right" around when I switch from the "scientific" to the "mathematical" contexts, even if I do so in the same sentence. Thus leading to a construction like this: "mathematical theories are always right, according to the mathematical definition of 'right'. Scientific theories are always right, according to the scientific definition of 'right'." You require that I say this sentence, instead of the sentence I said.
The problem is that the sentence I did say is still true, and you know it. I wasn't using the scientific definition of "right" in the first place, and I won't apologize for this.
I guess one implication of the definition of "right" you'd force me to use is that, say, Newton's theories were "right" back in the 1700s, just not now. In fact, all scientific theories are "right" as long as they gain consensus acceptance for a reasonable period of time. I guess I could protest about all this, about why you think it disproves anything I said (hint: it doesn't; you switched definitions on me), and in particular just how the heck it's supposed to related to putting "evolution is a theory" in front of science textbooks, but you know what?
I get bored. I don't think you have an actual point to make anyway.
Says who?
The disclaimer you defend is targeted at evolution, period.
So? Is the disclaimer false? We're back to square one here.
That you have, since coming on the thread, said that you would allow similar disclaimers on every other "theory," including the "theory" that your great-great- great-great grandparents once existed, is a throw-in. That is, it's a meaningless concession to get to a coveted goal.
It is? I don't know quite what you mean. What is my "coveted goal", Kreskin?
Anyway, even if you're right about whatever it is you think my sinister motives and "meaningless concessions" are, that still wouldn't prove a damn thing about whether it's ok for that state school board to put the disclaimer thingy.
Seriously, why do you think that proving stuff (or guessing stuff) about my biography will help prove that that state's school board decision is wrong?
Anyway, the goal is to smear evolution, your target,
Evolution is "my target"? Says who?
Perhaps you haven't noticed, but if you look at my various posts on this thread you'll probably see that I basically believe in "evolution". It's hilarious how wrong you are, and how hard you're working to grasp at such pointless straws.
You honestly do seem to think that ad hominem is a persuasive form of argument. If you can just prove that I'm a creationist fundie, then you'll win the argument!!1 Right?
There are enough ignorant people out there that "only a theory" will suffice for now.
I agree. See, I've heard many ignorant people who say things like "EVOLUTION IS INCONTROVERTIBLE SCIENTIFIC FACT". The minor, painless, truthful act of telling them that it's a theory will improve their knowledge. And that's all I'm interested in. What are you interested in, Kreskin? (I mean, besides weak and pathetic attempts at mind-reading....)
Your protests that I can't see what is going on here are laughable. Anybody can see what is going on here.
Well, I'm sure laughing. I don't know what the heck you're talking about. What's "going on here"? Seriously, what are you talking about?
You gotta read the thread before posting. Bruno was discussed.
In any sense of the word? Not even the sense of the word in which "true" is taken to mean "consistent with the assumptions of the established framework of discussion"?
Of course, by this standard, your post is not "true", since you've contradicted yourself. ;-P
I know, I know, you're going to get back to me (as Physicist did) with your detailed intricate view of how I should be defining "true" and "right". And I suppose that under your appropriately bizarre definition of "true", I won't be allowed to say that the Mean Value Theorem (or, for that matter, "2+2=4") is "true", for some reason.
You know what? I'm not interested. I think you know what I am saying, and know that what I am saying is unobjectionable, but you would just like to be a nuisance and/or show off.
Save it.
Granted.
I should've just said (rather, more strongly emphasized) "mathematical theories do indeed need disclaimers too", that would have nipped the show-offs in the bud. Well, maybe.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.