durangodawood
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For future reference: you wont go broke underestimating my math knowledge.Quantum field theories sometimes make use of Grassmann variables. Numbers that are anticommutating, i.e. xy = -yx
With the interesting result that xx = -xx = 0, for all Grassmann numbers.
Speculating (I haven't really thought about this), it seems to me that it's only in the hypothesising or model-making stage that we find may find concepts like an external reality to be useful, though not essential; the whole process would work just as well if ...
OK... but I don't see how that's relevant to the post it was responding to - what has Noble's forward to do with whether the 'axioms' of science are foundational or necessary?Not that I have any chance of changing your mind, but I do disagree, and I take some comfort in not being alone. Rather than mounting an argument, I'll simply quote from the Foreward of Longo's book, which was written by the Oxford biologist Denis Noble.
My apologies for the length of it.
During most of the twentieth century experimental and theoretical biologists lived separate lives. As the authors of this book express it, "there was a belief that experimental and theoretical thinking could be decoupled." This was a strange divorce. No other science has experienced such a separation. It is inconceivable that physical experiments could be done without extensive mathematical theory being used to give quantitative and conceptual expression to the ideas that motivate the questions that experimentalists try to answer. It would be impossible for the physicists at the large hadron collider, for example, to search for what we call the Higgs boson without the theoretical background that can make sense of what the Higgs boson could be.
From there he goes on to make several interesting comments about biology. For example, that "[evolution] does not make specific predictions in the way in which the Higgs boson [does] ... evolution is more that of a general framework within which biology is interpreted." Further, while biology does have theories - many theories - they are not subject to any "theoretical construct", they are "not formulated [as theories]", rather they are "presented as fact, a fait accompli."
He concludes then, that "There is a need for a general theory of biological objects and their dynamics. This book is a major step in achieving that aim."
With respect to this thread and the articles referenced, it was not specifically the work of Strippoli from 2005 that intrigued, but what Sverdlov did with it (and other information) in the second paper in formulating "unsolvable problems" in biology. In the same way, the uncertainty principle of physics is only interesting because of the unsolvable problems it identifies.
I'm not trying to establish some exact equivalency between the two, but as soon as one establishes a principle, it not only tells you what you can do, but what you can't do. That was one of Ana Soto's original complaints about her cancer research. Researcher 1 uses data set 1 to make conclusion 1, which conflicts with what researcher 2 concluded from data set 2. And there was no theory of biology that could mediate the conflict. It was just a battle of numbers with no end in sight.
OK... but I don't see how that's relevant to the post it was responding to - what has Noble's forward to do with whether the 'axioms' of science are foundational or necessary?
Those are theory models & hypotheses, not axioms.Because, repeating and paraphrasing part of what I quoted from Noble above, they give quantitative and conceptual expression to the ideas that motivate the questions that experimentalists try to answer. It's impossible to search for a scientific object without the theoretical background that can make sense of what it could be.
Flatness may be an axiom of Euclidean geometry, but the curvature or flatness of space is not an axiom of physics - we make observations to discover the geometry of space.Flat space is different than hyperbolic space. Changing an axiom results in a change from one to the other.
If we consider that geology proper began in the early part of the 19th century then for most of the time geology has been practiced it has been either in the absence of any theoretical background, or using theoretical backgrounds that were largely bogus. Despite these supposed limitations a vast body of observations were gathered that allowed for the emergence of plate tectonic theory in the 1950's and 1960's. That theoretical resource now illuminated a wealth of extant observations beyond those on which the theory was founded. This experience contradicts your assertion.It's impossible to search for a scientific object without the theoretical background that can make sense of what it could be.
Flatness may be an axiom of Euclidean geometry, but the curvature or flatness of space is not an axiom of physics - we make observations to discover the geometry of space.
I'm inclined to agree with you--"common sense" Newtonian space was certainly taken for granted in the early days of physics. But I have lost track of the point you were trying to make with it.I disagree. You're inventing a history of science that never happened to fit your philosophy of what should have happened.
As I said, I knew I wouldn't be able to change your mind. I've mentioned some references to get you started if you decide to look into it further. Based on this last post, I suppose I should add some historical references as well. To start with, maybe: Einstein's Jury: The Race to Test Relativity by Jeffrey Crelinsten or Einstein's Masterwork: 1915 and the General Theory of Relativity by John Gribbin.
Good luck.
If we consider that geology proper began in the early part of the 19th century then for most of the time geology has been practiced it has been either in the absence of any theoretical background, or using theoretical backgrounds that were largely bogus. Despite these supposed limitations a vast body of observations were gathered that allowed for the emergence of plate tectonic theory in the 1950's and 1960's. That theoretical resource now illuminated a wealth of extant observations beyond those on which the theory was founded. This experience contradicts your assertion.
But I have lost track of the point you were trying to make with it.
I'm not talking about the history of science, but about whether or not what are often taken to be its axioms really are axioms. I'm open to reasonable argument about that.I disagree. You're inventing a history of science that never happened to fit your philosophy of what should have happened.
My mind isn't made up, it's open to change if I get a reasonable argument. At present, I suspect that what are commonly taken to be the axioms of science are not foundational.As I said, I knew I wouldn't be able to change your mind. I've mentioned some references to get you started if you decide to look into it further. Based on this last post, I suppose I should add some historical references as well. To start with, maybe: Einstein's Jury: The Race to Test Relativity by Jeffrey Crelinsten or Einstein's Masterwork: 1915 and the General Theory of Relativity by John Gribbin.
That was my impression. Here is why.I just started rambling
Here are some of the "scientific objects" related to plate tectonics that were observed before the the theory of plate tectonics was proposed. (There are a bunch more.)It's impossible to search for a scientific object without the theoretical background that can make sense of what it could be.
Unfortunately for your argument this does not reflect what occurred. For example, no one was looking for evidence of ocean floor spreading. Magnetic striping ( a scientific object) was discovered with no explanation for it till the work of Vine & Mathews and another pair whose names temporarily escape me.The data they had to date was insufficient, because they didn't know what corroborating data to look for until someone suggested the phenomena: observed, asked a question, formulated a hypothesis, and designed a test. Sound familiar?
I'm not talking about what was commonly assumed at one time or other, but whether there are any foundational axioms without which science can not proceed.I'm inclined to agree with you--"common sense" Newtonian space was certainly taken for granted in the early days of physics. But I have lost track of the point you were trying to make with it.
In that case, you undermine your own point that flat space was ever an axiom, and given your response, it appears that I mean all the way back to the OP after all.That is a problem in Internet forums.
Some are arguing science has no axioms. They seem to equate empirical observation with truth. If we see it and name a principle after it, that's a truth, not an axiom.
Ain't never gonna buy that.
... Or did you mean way back to the OP?
Indeed, but what's the point being made?I'm not talking about what was commonly assumed at one time or other, but whether there are any foundational axioms without which science can not proceed.
That was my impression.
Here are some of the "scientific objects" related to plate tectonics that were observed before the the theory of plate tectonics was proposed. (There are a bunch more.)
Either your assertion is refuted by this, or your assertion has been poorly phrased and thus misunderstood by me. Feel free to restate it, or acknowledge the refutation. I'm comfortable with either.
- Restricted distribution of volcanic activity
- Benioff zones
- Mid-ocean ridges
- Discontinuities of tectonic zones across oceans
My mind isn't made up, it's open to change if I get a reasonable argument. At present, I suspect that what are commonly taken to be the axioms of science are not foundational.
If you disagree, present what you believe to be a foundational axiom of science and let's discuss it.
I think there's a useful distinction between an axiom of Science aka the scientific method. And the axioms or assumptions that are built into any particular model of some aspect of natural phenomena.
It's impossible for me to tell at this stage. When you introduced the term in passing, without explicit definition, I had to infer its meaning from your comments. It appeared as if the term was equivalent to observations, experimental results and the like. It now emerges from your comments, still with no definition, that it is closer to being a theory. I base this inference upon this:[*Note]: If I'm wrong about "scientific object", please correct me.
It seems you are establishing a direct equivalence of theory and scientific object. The trouble with that is you then seem to be saying "we can't have a theory unless we have a theory", which doesn't seem to take us anywhere.Regardless, what I am saying is that you are referring to observations and definitions, not a theory, not a "scientific object".
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