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Thread: An Irrefutable Definition of a Scientific Theory

  1. #1 An Irrefutable Definition of a Scientific Theory 
    Forum Freshman Shubee's Avatar
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    I'm in a debate that has boiled down to a need for an irrefutable definition of a "scientific theory." I thought that I would ask mathematicians and physicists because the precision and sophistication of their science is far above the many quasi-sciences.

    Here is what I want to know specifically and please forgive me in advance if you find my question contemptible. Is there an incontrovertible definition of a scientific theory that makes The Origin of Species by Charles Darwin a "scientific theory"? If so, what is that definition and please cite the source.

    Thanks for your help.

    Shubee


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  3. #2  
    DTV
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    A theory is a hypothesis supported by experimentation, observation, and logic that can predict the outcome of events and support other theories.

    http://www.fsteiger.com/theory.html
    http://www.notjustatheory.com/
    http://atheism.about.com/od/philosop...ificTheory.htm

    By the way, where is that debate? [/i]


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  4. #3  
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    Quote Originally Posted by DTV
    A theory is a hypothesis supported by experimentation, observation, and logic that can predict the outcome of events and support other theories.
    OK. Then please tell me about the experiments of Charles Darwin that led Darwin to publish The Origin of Species in 1859 and the experiments of Albert Einstein that led him to formulate the theory of relativity in 1905.

    I was looking for authoritative sources. Is it true that all celebrity scientists, like Albert Einstein, Richard Feynman, Steven Hawking and Richard Dawkins, known for popularizing science, have never defined science?

    Quote Originally Posted by DTV
    By the way, where is that debate?
    http://www.thescienceforum.com/The-T...ion-19999t.php

    I'm preparing for a comeback.
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  5. #4  
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    Quote Originally Posted by Shubee
    Quote Originally Posted by DTV
    A theory is a hypothesis supported by experimentation, observation, and logic that can predict the outcome of events and support other theories.
    OK. Then please tell me about the experiments of Charles Darwin that led Darwin to publish The Origin of Species in 1859 and the experiments of Albert Einstein that led him to formulate the theory of relativity in 1905.
    Well, observations rather than experiments. He looked at the features of species around the world, and in the fossil records. It's worth noting, though:

    -The origin of the species if a book, not a theory.
    -The modern theory of evolution is not necessarily the same as Darwin's; the thing about science is theories change over time to account for new evidence, or reviewing of old evidence.

    Quote Originally Posted by Shubee
    I was looking for authoritative sources. Is it true that all celebrity scientists, like Albert Einstein, Richard Feynman, Steven Hawking and Richard Dawkins, known for popularizing science, have never defined science?
    I've never seen a firefighter define fire, either. It's not important.

    Quote Originally Posted by Shubee
    I'm preparing for a comeback.
    Be aware you will still have to back up your own claims with evidence, and not just attack existing theories.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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  6. #5  
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    e=mc2 is a hypothesis, supported by mathematics and experimentation, and so it is considered a theory
    Dick, be Frank.

    Ambiguity Kills.
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  7. #6  
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    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by Shubee
    Quote Originally Posted by DTV
    A theory is a hypothesis supported by experimentation, observation, and logic that can predict the outcome of events and support other theories.
    OK. Then please tell me about the experiments of Charles Darwin that led Darwin to publish The Origin of Species in 1859 and the experiments of Albert Einstein that led him to formulate the theory of relativity in 1905.
    Well, observations rather than experiments.
    In other words, I wasn't given a straight, well-thought-out answer or The Origin of Species did not contain a scientific theory in 1859.
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  8. #7  
    Forum Professor marcusclayman's Avatar
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    experiments are really just observations in a controlled setting
    Dick, be Frank.

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  9. #8  
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    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by Shubee
    I was looking for authoritative sources. Is it true that all celebrity scientists, like Albert Einstein, Richard Feynman, Steven Hawking and Richard Dawkins, known for popularizing science, have never defined science?
    I've never seen a firefighter define fire, either. It's not important.
    There are many that share your uncritical view; Richard Dawkins is one. He said:

    "The particular variety of truth that concerns me is scientific truth. And that is what I mostly want to talk about today. So what is this thing called science? My own definition is the study of what is true about the real world." Richard Dawkins, University of Valencia, March 31, 2009.

    That's very disappointing. Surely Dawkins has a definition better than that!
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  10. #9  
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    Oh god, please... I do not care about Dawkins nor what he has to say. A scientific theory is one that is entirely open to change. It is never concrete nor absolute. A theory is supported by evidence, observations, and experiments where applicable. Darwin's theory of evolution was a conjecture which he made in 1859. It has since become a theory that is supported by further observations and discovered evidence. THERE ARE NO EXPERIMENTS FOR EVOLUTION!!! It is not that kind of theory! It's a theory that will require observation and evidence of change. That is all. Devolution, however, is simply a counter-intuitive argument that you are making that has no grounding in science, sorry.
    Wise men speak because they have something to say; Fools, because they have to say something.
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  11. #10  
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    Quote Originally Posted by Arcane_Mathematician
    Oh god, please... I do not care about Dawkins nor what he has to say.
    I feel the same way.

    Quote Originally Posted by Arcane_Mathematician
    A scientific theory is one that is entirely open to change. It is never concrete nor absolute.
    Does that mean you are opposed to calling the study of all mathematically consistent universes, science?

    Quote Originally Posted by Arcane_Mathematician
    A theory is supported by evidence, observations, and experiments where applicable.
    There is direct evidence that "the ancestor of brainless starfish and sea urchins had a brain" and no direct evidence that any species has transitioned from a lower to a higher form. Therefore, by your definition, the theory of devolution is a scientific theory.

    Quote Originally Posted by Arcane_Mathematician
    THERE ARE NO EXPERIMENTS FOR EVOLUTION!!! It is not that kind of theory!
    It's always nice to meet a well-informed mathematician.

    Quote Originally Posted by Arcane_Mathematician
    Devolution, however, is simply a counter-intuitive argument that you are making that has no grounding in science, sorry.
    All mathematicians should understand counter-intuitive games, once the rules are spelled out. To make devolution perfectly consistent with David Hilbert's philosophy of physics only requires precisely stated axioms about the world and logical consistency within a clearly defined domain of applicability.
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  12. #11  
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    there are plenty of experiments for evolution

    for example, genetic experiments gives us a good idea of what creatures are related

    for example, amongst humans: we can make a generalized timeline of human origin and migrations up until the present

    we can do the same with other creatures, beyond the point that a species becomes sexually isolated and becomes it's own species it's just much more complex, and will take MUCH more time and funding.

    There is a study going on near New Zealand(I think?), two of the same species of birds, each with it's own color pattern and habitat, separated only by a few miles of sea, do not consider each other sexual rivals, showing that they no longer mate, even though they could. The theory goes that these two groups will eventually reach the point when they cannot mate with each other. We must wait and see. The experiment is in progress.
    Dick, be Frank.

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  13. #12  
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    Quote Originally Posted by marcusclayman
    there are plenty of experiments for evolution
    The problem is that science should be expressed in precise language, which indicates clear thinking, and that your statements are terribly imprecise.
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  14. #13  
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    How about I give you some links to follow?

    E. Coli Evolution Experiment

    Antibiotic Resistance

    Human Genome Project

    Enjoy.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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  15. #14  
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    Quote Originally Posted by Shubee
    Quote Originally Posted by Arcane_Mathematician
    A theory is supported by evidence, observations, and experiments where applicable.
    There is direct evidence that "the ancestor of brainless starfish and sea urchins had a brain" and no direct evidence that any species has transitioned from a lower to a higher form. Therefore, by your definition, the theory of devolution is a scientific theory.
    Not even remotely so. You have identified a possible link between two variables, but have not shown that the link really exists, nor that the evidence actually supports your theory. Lack of evidence that disproves your theory does not count as evidence for; otherwise we have a large number of gods which are scientifically proven. You also haven't defined what "higher" and "lower" lifeforms are.

    Quote Originally Posted by Shubee
    Quote Originally Posted by Arcane_Mathematician
    THERE ARE NO EXPERIMENTS FOR EVOLUTION!!! It is not that kind of theory!
    It's always nice to meet a well-informed mathematician.
    He means for the original theory of evolution; that species have changed over time. At the time when evolution became generally acepted in biology, there were no experiments to be undertaken regarding evolution, because the DNA molecule had not been identified so change could nto be measured.

    Experiments exist today, but generally to measure genetic change rather than to prove the change occurs.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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  16. #15  
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    Science should be expressed in precise language, which facilitates clear thinking. One obvious clue that many of the quasi-sciences are subpar is their quasi-scientists giving flowery and/or terribly imprecise definitions of what science is, and what a scientific theory is, in their discipline. Therefore, in the interest of promoting all true science, I have devised the following argument for a general definition of a scientific theory.

    All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the highest science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires a logically consistent set of definitions and precisely stated fundamental axioms that generates a plethora of coherent, precisely stated physical concepts and ideas.
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  17. #16  
    Reptile Dysfunction drowsy turtle's Avatar
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    Whether or not devolution counts as a theory, you're still talking out your arse the whole time. Instead of trying to change the rules to persuade people that devolution is a theory which is not supported by (any) evidence, try gathering evidence instead.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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  18. #17  
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    Quote Originally Posted by Shubee
    Quote Originally Posted by Arcane_Mathematician
    A scientific theory is one that is entirely open to change. It is never concrete nor absolute.
    Does that mean you are opposed to calling the study of all mathematically consistent universes, science?
    No, but I will refuse to say their conjectures are theories until there is experimentation done, likewise with Darwin's conjecture.

    Quote Originally Posted by Shubee
    Quote Originally Posted by Arcane_Mathematician
    A theory is supported by evidence, observations, and experiments where applicable.
    There is direct evidence that "the ancestor of brainless starfish and sea urchins had a brain" and no direct evidence that any species has transitioned from a lower to a higher form. Therefore, by your definition, the theory of devolution is a scientific theory.
    No. By my definition and the definition of evolution, Evolution is a theory and is what you are describing. Never in the theory does it give directionality to the type of life form that will be produced through it's process. Devolution makes as much sense to me a Decceleration, it's a word that someone cooked up in total ignorance to the meaning of the word they wished to counter.

    Quote Originally Posted by Shubee
    Quote Originally Posted by Arcane_Mathematician
    Devolution, however, is simply a counter-intuitive argument that you are making that has no grounding in science, sorry.
    All mathematicians should understand counter-intuitive games, once the rules are spelled out. To make devolution perfectly consistent with David Hilbert's philosophy of physics only requires precisely stated axioms about the world and logical consistency within a clearly defined domain of applicability.
    Alright, Shubee, there is a discrete difference between Mathematics and the natural sciences. Hilbert was a "pure" Mathematician, mind you, and had a mathematical view of physics. He also never really developed anything in physics, he only more discretely defined the math behind some of Einstein's conjectures. And fyi Shubee, those philosophies of his you so nicely linked were formed before he had ANY formal training or interest in physics. Those are the philosophies on a mathematician imposed upon a natural science, hardly valuable in this place.

    Quote Originally Posted by drowsy turtle
    He means for the original theory of evolution; that species have changed over time. At the time when evolution became generally acepted in biology, there were no experiments to be undertaken regarding evolution, because the DNA molecule had not been identified so change could nto be measured.

    Experiments exist today, but generally to measure genetic change rather than to prove the change occurs.
    I was speaking only of macro species, actually.

    At this point, an experiment to prove the existence of evolution is actually non-existent on a non-microbial scale. It takes too many generations to see which mutation will actually be the best adapted to survive in the long run, you can only get loose data and relatively small differences that can be observed. Only on the bacterial and viral scale can we truly measure the success of evolution, but to apply these experiments to macro species isn't going to happen, it takes too long for the reproductive success to make itself noted (a 100-year experiment is slightly impractical, after all). It is worth noting that we have observed rapid evolutionary changes to occur in some species, and we do know it happens, though I would postulate it happens only when absolutely necessary. I agree with you turtle, and it just so happens that shubee is digging a rather big hole for himself here.
    Wise men speak because they have something to say; Fools, because they have to say something.
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  19. #18  
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    "The problem is that science should be expressed in precise language, which indicates clear thinking, and that your statements are terribly imprecise."

    This is not science, this is a discussion on some aspects of science. Your statements are equally vague. Notice how the accuser says we are "too vague" yet does not point out specific statements. Here's some vague sarcasm: your definition of precision is beyond my comprehension.
    Dick, be Frank.

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  20. #19  
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    Quote Originally Posted by Shubee
    Quote Originally Posted by DTV
    A theory is a hypothesis supported by experimentation, observation, and logic that can predict the outcome of events and support other theories.
    OK. Then please tell me about the experiments of Charles Darwin that led Darwin to publish The Origin of Species in 1859 and the experiments of Albert Einstein that led him to formulate the theory of relativity in 1905.
    At the moment of formulation, it would still have been considered a "hypothesis", not a "theory". It was only after other scientists started doing genuine experimentation that these were later redefined to be "theories".

    That's how it always works. Scientific ideas always start out as mere hypothesis, and later graduate into being theories. Sometimes even the person who proposed the idea is long dead by that time, but we still give them credit and call it their "theory", because they came up with it.

    Quote Originally Posted by Shubee
    Science should be expressed in precise language, which facilitates clear thinking. One obvious clue that many of the quasi-sciences are subpar is their quasi-scientists giving flowery and/or terribly imprecise definitions of what science is, and what a scientific theory is, in their discipline. Therefore, in the interest of promoting all true science, I have devised the following argument for a general definition of a scientific theory.

    All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the highest science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires a logically consistent set of definitions and precisely stated fundamental axioms that generates a plethora of coherent, precisely stated physical concepts and ideas.
    I've taken some interesting classes devoted to "philosophy of science" or "epistemology", and unfortunately, science has no straightforward, concise, definition that satisfies everyone. Some big names like Karl Popper, Thomas Kuhn, Baas Van Fraasen, Grover Maxwell.......... and quite a few other people..... have written extensively on the topic without really arriving at any universally accepted conclusions.

    In general, I would stick with DTV's definition. It's probably the most agreed upon.
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  21. #20  
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    Quote Originally Posted by Shubee
    Science should be expressed in precise language, which facilitates clear thinking. One obvious clue that many of the quasi-sciences are subpar is their quasi-scientists giving flowery and/or terribly imprecise definitions of what science is, and what a scientific theory is, in their discipline. Therefore, in the interest of promoting all true science, I have devised the following argument for a general definition of a scientific theory.

    All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the highest science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires a logically consistent set of definitions and precisely stated fundamental axioms that generates a plethora of coherent, precisely stated physical concepts and ideas.
    Thank you all. After a brief struggle, this is my irrefutable definition of a scientific theory.
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  22. #21  
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    that is your personal definition, not an irrefutable one. Please, though, delude yourself further.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  23. #22  
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    Quote Originally Posted by Shubee
    Quote Originally Posted by Shubee
    Science should be expressed in precise language, which facilitates clear thinking. One obvious clue that many of the quasi-sciences are subpar is their quasi-scientists giving flowery and/or terribly imprecise definitions of what science is, and what a scientific theory is, in their discipline. Therefore, in the interest of promoting all true science, I have devised the following argument for a general definition of a scientific theory.

    All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the highest science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires a logically consistent set of definitions and precisely stated fundamental axioms that generates a plethora of coherent, precisely stated physical concepts and ideas.
    Thank you all. After a brief struggle, this is my irrefutable definition of a scientific theory.
    Whatever. If you want devolution to become accepted, you'll still need evidence.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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  24. #23  
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    No position in science should be incapable of being refuted or disputed which is what "irrefutable" means.

    Indeed, the definition of the word "theory" in science is held by the consensus of the overwhelming majority of those doing science to be a way of describing that which contains facts, hypotheses that have undergone rigorous testing and attempts to falsify, and over-arching explanations which often tie the theory to other theories.

    It is curious, however not unexpected, that a creationist would attempt to pigeonhole those who embrace science into a definition that the creationist can exploit by inserting the strawman element of "irrefutable." In the doctrines and superstitions of religions such as various cults of Christianity, there exist many "irrefutable" and necessarily unfalsifiable qualities, characteristics and "explanations" (inverted commas necessary). This isn't so with the reality-based community of science. All theories, facts, laws, and explanations are open to revision and even to being discarded with the advent of new evidence.

    Such is the strength of science.
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  25. #24  
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    Quote Originally Posted by Shubee
    All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the highest science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires a logically consistent set of definitions and precisely stated fundamental axioms that generates a plethora of coherent, precisely stated physical concepts and ideas.
    You have totally misunderstood both science and Hilbert.

    He is suggesting an axiomatic structure for science similar to that used to develop a mathematical theory. But he is NOT suggesting that only a set of axioms are required in a successful scientific theory.

    A scientific theory requires not only a consistent mathematical structure with which to make predictions, but also it requires that the predictions be supported by what is actually observed to occur in nature. It is quite possible to formulate a mathematically consistent "theory" that fails to describe nature. From a purist perspective Newtonian mechancis is such a theory. There are others with far less connection to reality.

    It is also worth noting that mathematics is NOT science. It is a different animal altogether. The primary difference is that mathematics relies on proof, and has no reliance on experiment or any natural phenomena.
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  26. #25  
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Shubee
    All mathematicians agree that mathematics is anything that enables the creation of mathematical theorems, once precise definitions are given. Logically then, a scientific theory may be defined as any endeavor that mimics the highest science according to David Hilbert's philosophy of physics. Thus, for those that think like mathematicians, a scientific theory only requires a logically consistent set of definitions and precisely stated fundamental axioms that generates a plethora of coherent, precisely stated physical concepts and ideas.
    You have totally misunderstood both science and Hilbert.

    He is suggesting an axiomatic structure for science similar to that used to develop a mathematical theory.
    And I too am arguing for an axiomatic structure in science. And it's obvious that my detractors are against that proposal.

    Quote Originally Posted by DrRocket
    But he is NOT suggesting that only a set of axioms are required in a successful scientific theory.
    Hilbert argued for the study of all logically consistent theories in physics. And who am I to disagree with the man that taught Einstein how to derive the equations of general relativity?

    Quote Originally Posted by DrRocket
    It is also worth noting that mathematics is NOT science.
    Dictionary.com disagrees with you. Read their entry on science.

    Especially note entry #2:

    science
    noun
    1. a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences.
    2. systematic knowledge of the physical or material world gained through observation and experimentation.


    That means that if your knowledge of the physical world isn't organized systematically, then it's not science.
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  27. #26  
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    Quote Originally Posted by Shubee
    Quote Originally Posted by DrRocket
    et"]But he is NOT suggesting that only a set of axioms are required in a successful scientific theory.
    Hilbert argued for the study of all logically consistent theories in physics. And who am I to disagree with the man that taught Einstein how to derive the equations of general relativity?
    Hilbert did not teach Einstein how to derive the field equations for general relativity. They were in fact competitors in that particular endeavor.

    You are confusing an axiomatic approach to physics with the basic science of physics. They are not the same thing.

    While it is quite useful to have an axiomatic treatment of physical theories, it is only by experiment that theories are accepted as true. The axiomatic approach simply provides a clean way to develop the theoretical models.

    Quote Originally Posted by DrRocket
    It is also worth noting that mathematics is NOT science.
    Quote Originally Posted by Shubee
    Dictionary.com disagrees with you. Read their entry on science.
    That would make your dictionary wrong. Neither I nor any other professional mathematician of my acquaintence (and I know a LOT of mathematicians) consider mathematics to be a science. It is closely allied, but mathematics is distinguished from science by reliance on logical proof rather than empirical evidence. This embracihng of logic and eschewing of experiment is a clearly distinguishing feature.

    It is also worth noting that while the axiomatization of physics was one of the original Hilbert problems, it remains unaccomplished. It is probably farther away now, with the advent of newer physical theories than it was when Hilbert first proposed it.
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  28. #27  
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    Quote Originally Posted by DrRocket
    Hilbert did not teach Einstein how to derive the field equations for general relativity. They were in fact competitors in that particular endeavor.
    That's not how Hilbert tells the story.

    Quote Originally Posted by DrRocket
    You are confusing an axiomatic approach to physics with the basic science of physics. They are not the same thing.
    You are imputing all kinds of crazy notions to me things that I did not say.

    Quote Originally Posted by DrRocket
    While it is quite useful to have an axiomatic treatment of physical theories, it is only by experiment that theories are accepted as true.
    Tell that to physicists that believe in string theory, spacetime curvature, dark matter and black holes.

    Quote Originally Posted by DrRocket
    Quote Originally Posted by DrRocket
    It is also worth noting that mathematics is NOT science.
    Quote Originally Posted by Shubee
    Dictionary.com disagrees with you. Read their entry on science.
    That would make your dictionary wrong. Neither I nor any other professional mathematician of my acquaintence (and I know a LOT of mathematicians) consider mathematics to be a science.
    To Hilbert, geometry was a science and the whole point of Hilbert's famous sixth problem was to make all science mathematics.
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  29. #28  
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    Quote Originally Posted by Shubee

    That's not how Hilbert tells the story.
    Hilbert is dead. The record shows that Hilbert and Einstein were in competition, that Hilbert published slightly ahead of Einstein, but made some revisions and that Hilbert himself credited Einstein fully as the discoverer of general relativity.

    Hilbert and Einstein became friends after the publication of the general theory of relativity, but the mathematician who helped Einstein with tensor calculus was not Hilbert but rather Marcel Grossman.

    Quote Originally Posted by Shubee
    Quote Originally Posted by DrRocket
    You are confusing an axiomatic approach to physics with the basic science of physics. They are not the same thing.
    You are imputing all kinds of crazy notions to me things that I did not say.
    Nope. I am simply addressing that which follows from your basic statements.

    Quote Originally Posted by DrRocket
    Shubee}
    Quote Originally Posted by DrRocket
    While it is quite useful to have an axiomatic treatment of physical theories, it is only by experiment that theories are accepted as true.
    Tell that to physicists that believe in string theory, spacetime curvature, dark matter and black holes.
    I would be quite happy happy to and have done so.

    You are really confused on several points here.

    1. Spacetime curvature is a key elements in general relativity and general relativity is abundantly supported by experimental evidence. http://en.wikipedia.org/wiki/Tests_o...ral_relativity

    2. Black holes are a prediction of general relativity and are supported by the evidence that supports that theory. There is also observational evidence for the existence of black holes, particularly in the center of many galaxies. This evidence provides additional confirmation of general relativity as well as black holes.

    http://science.nasa.gov/newhome/head...t06nov97_1.htm

    http://www.crystalinks.com/black_holes.html

    http://www.sciencedaily.com/releases...0111182222.htm

    3. The dark matter hypothesis is a direct result of empirical data. In fact there is no theoretical prediction of its existence. We have NO theory, just observation and speculation. Since it is not understood, it is simply named. Yoiu cannot rely on theory to justify dark matter. There is none. Theorists are struggling to determine what it might be and to fit it into the available theoretical framework.
    http://web.mit.edu/~redingtn/www/net...r/012/012.html

    4. String theory is not yet physics. The next significant testable prediction of string theory will be the first one. It is not rigorous mathematics either, at least not yet. No one can even provide a clear rigorous definition of what string theory really is. The biggest open question in M-theory is "What is M-theory?" It is neither axiomatic nor physics.

    What string theory and M-theory are are general avenues of research that may eventually prove to be fundamental physics. Or they may die on the vine. They have provided some very interesting and fruitful problems for research in pure mathematics and in recognition of that, and his work on the classification of manifolds Ed Witten was awarded a Fields Medal.

    Quote Originally Posted by DrRocket
    Quote Originally Posted by DrRocket
    It is also worth noting that mathematics is NOT science.
    Quote Originally Posted by Shubee
    Dictionary.com disagrees with you. Read their entry on science.
    That would make your dictionary wrong. Neither I nor any other professional mathematician of my acquaintence (and I know a LOT of mathematicians) consider mathematics to be a science.
    To Hilbert, geometry was a science and the whole point of Hilbert's famous sixth problem was to make all science mathematics.[/quote:59da7b1072]

    Hilbert was quite so ambitious as to directly call for the axiomatizatioin of all science, only those that used a significant amount of mathematics at the time of his address. That was basically classical mechanics and electrodynamics, but the idea extends easily to modern physics as well. However, his problem remains open.

    Asking for axiomatization as a goal, for mature branches of physics is one thing. But confusing mathematics with science is quite another. The two are, as noted earlier, quite distinct.

    As a mathematician I am quite sympathetic towards Hilbert's objective, and quite comfortable with axiomatic approaches. But axiomatics are not appicable until the basic science is fairly well understood. Physics is not a deductive science. The formulation of the basic principles is the act of determining the axioms that one would use in an axiomatic approach.

    In truth, mathematical research is not really deductive either. What one typically does is "guess" the result, based on insight and intuition and then apply rigorous logic to prove that the guess is correct. However, it only the final polished proof that is usually published, and all the dirty work is swept under the rug. You don't get to see the creative process unless you are involved in it.

    The flip side of this issue is that some physicists fail to recognize the role of mathematical rigor is reasoning as it relates to physical theories and are quite content to push around symbols that they don't undetrstand in ways that cannot be justified. There is a role for axiomatization of physical theories, but it is largely an after-the-fact enterprise. That is completely consistent with Hilbert's statement of his sixth problem.
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  30. #29  
    Forum Radioactive Isotope MagiMaster's Avatar
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    @Shubee, a brief analogy:

    Science:Mathematics :: Inductioneduction

    Go look it up.

    Edit: Also, check out this site.
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  31. #30  
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    Quote Originally Posted by MagiMaster
    Science:Mathematics :: Inductioneduction
    That's a nice equation but please realize that deduction is used in science all the time. Also, it's not unbelievable that the brains of most mathematicians are wired to think inductively.
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  32. #31  
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    wired to think inductively... are you serious?

    is there evidence of this?
    Dick, be Frank.

    Ambiguity Kills.
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  33. #32  
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    Don't all humans think inductively and deductively, naturally?
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    Was the claim not that mathematicians are wired to think inductively? Was this not to imply that that mathematicians are different in this feature, than those in other specialized fields?

    Anyway, I'm not a neurologist, I'm not fit to make generalizations about how people are wired.

    Do you have support for your claims?
    Dick, be Frank.

    Ambiguity Kills.
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  35. #34  
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    Quote Originally Posted by marcusclayman
    Was the claim not that mathematicians are wired to think inductively? Was this not to imply that that mathematicians are different in this feature, than those in other specialized fields?

    Anyway, I'm not a neurologist, I'm not fit to make generalizations about how people are wired.

    Do you have support for your claims?
    Neurology aside, the process used in research mathematics is a bit of both. But the hard part is the inductive piece.

    Mathematical research first proceeds inductively. The mathematician first "guesses" a result based on intuition and insight. He then applies deduction and logic to prove that the guess is correct. What you see in research papers and text books is usually only the final polished proof which is the deductive step that proves the guess. You rarely see the inductive process by which the result was discovered in the first place.

    Since the published results show only half the process, most people have a very distorted view of how mathematics is actually done. The only people who usually see the entire process are research mathematicians themselves.

    The creative and most difficult aspect of research mathematics is the inductive, "guessing", part.
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  36. #35  
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    You're missing the point Shubee, he meant that the two concepts are related, rather intricately as it were, but also that they are not the same. Induction and Deduction are very similar but by no means are they the same, and that's what the analogy was for.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  37. #36  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I agree that both scientists and mathematicians use both induction and deduction. I was referring more to the fields themselves. Science is more inductive than deductive because we can never be sure we have the right axioms to make deductions from. Mathematics is more deductive than inductive because we start with the premise that, right or wrong, what we want to know is what can be deduced from a given set of axioms. (Broad generalizations there, so don't take me too literally.)

    In any case, mathematics will always be an important tool for scientists, and a mathematician will always need some insight and intuition to find something new.
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    Science can't ever be axiomatic because it's based on observation of the natural world, and observation is never totally infallible. Mathematics, on the other hand, isn't based on observation of anything external to itself.

    Quote Originally Posted by Shubee
    Quote Originally Posted by DrRocket
    But he is NOT suggesting that only a set of axioms are required in a successful scientific theory.
    Hilbert argued for the study of all logically consistent theories in physics. And who am I to disagree with the man that taught Einstein how to derive the equations of general relativity?
    Even if Hilbert were one of Einstein's teachers, that doesn't make him some kind of an infallible authority you can refer to. Besides, you shouldn't be looking for them, or defining people as sources of truth.

    Probably a lot of the reason certain now-famous scientists like Galileo were persecuted is because they weren't the right "who". People get it in their head that only one group of people is entitled to have ideas.
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  39. #38  
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    "Science can't ever be axiomatic because it's based on observation of the natural world,"

    "it's based on observation of the natural world" is an axiom
    Dick, be Frank.

    Ambiguity Kills.
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    That is a very loosely defined axiom, not a rigid one like what you experience in the field of Mathematics.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  41. #40  
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    Quote Originally Posted by kojax
    Science can't ever be axiomatic because it's based on observation of the natural world, and observation is never totally infallible. Mathematics, on the other hand, isn't based on observation of anything external to itself.
    This is true, but it misses Hilbert's point.

    Hilbert was not arguing for the axiomatization of science. It is pretty clear that such an idea would not work, and for the reason that you stated.

    What he wanted to do was axiomatize the known laws of physics, not the research process. For instance, Newtonian mechanics is easily axiomatized. That is basically what Newton did. The axiomatization comes after the fact, after the basic physics is known. It serves merely to convert a loose mathematical model into a rigorous one.

    It is not a bad idea. But it has not been accomplished, and may never be.
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