The Underlying Structure of Knowledge

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I could spend literally pages just setting everything up for the question, but I will rather ask then explain. What is the best (efficient/accurate) method of obtaining scientific knowledge?

Can the laws of physics (and, in turn, presumably everything else) be deduced and proven purely by logical thought (i.e. derived directly from the law of non-contradiction)? Is empiricism the right way to go (finding no underlying logic, just the simplest explanation of the data)?

If it is a hybrid of reason and empiricism (which, for all practical purposes, I believe is true), where do you draw the lines and domains of each? Surely there can be no gray area in physics!

As for what I believe, I believe that, despite an infinite amount of irreducible truth (proven by Gödel: http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems ), all of it can be found with an infinite amount of foresight, time, and energies, which the human race apparently does not have. Therefore, I believe that the majority of the laws of physics (or the laws by which they are chosen) can be found independent of any observational proof, merely from the law of non-contradiction. However, since we are not up to this task, a more moderate method should be used, namely a mixture between the pure scientific method and pure logical structure. My only problem is that I have no clue how to combine this perfectly, since it takes such geniuses as Newton and Einstein to even attempt this. Perhaps some of you, if interested, can help me?

 
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I don’t think the old divide is helpful. If we wish to create the best scientific models, we must use both our rational and depend on empirical evidence. Thought experiments are useful, but empirically proven theories will always be more valid. I think the hybrid.

There are no grey areas, just areas of black and white really close together. The reason it is hard to draw the line is because the line is an arbitrary concept in the first place that probably shouldn’t have been drawn.

 
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That’s part of the problem with science is its need to classify and organize everything that may or may not be classifiable. We can argue that Science is dynamic, and thus makes adjustments and exceptions to make up for that flaw. Ultimately, modern science is only as good as its tools. That isn’t so bad, but the problem comes from who’s selecting the tools, why they’re being selected, and how they’re being used. Classification is one of those tools.

But I’m probably getting off topic.

 
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Scientific understanding is purely mathematical. Observation is a flawed way of proving anything, but rather a final point which now a days is not even required. physics has plenty of gray areas, but only because we do not at the moment understand the mathematical basis to separate the black from white…
(and current theory suggests we need 6th dimensional math to even start understanding the real nature of the universe…. good luck 4d is hard enough)

 
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I admit, I was a little mislead by this thread title (thinking we were going to talk more about neurological pathways and such) but it’s an interesting concept. My gut reaction, which will likely be corrected, is that we must have a hybrid of the two methods. For example, I don’t think it’s possible to deduce something like a gravitational constant or the atmospheric pressure on Earth or anything like that. Thus, some knowledge must be measured. However, measurement is never sufficient as proof of anything. If we are only interested in provable knowledge, then it must be deduced, though empirical evidence of course can help guide our deductions.

 
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why would you want to know ?
when i was a kid, i wished i could just absord the knowledge of book by a touch.
i guess i was frighten of the unknown for one thing, and on the other hand, taugh that an important man is someone who knows.

i guess time is the key to knowlegde. your own for sure, but that of mankind.
Newton & Einstein are figures, heroes, mythologies of the genius… but they were men, working on other men’s work, generations of other men’s work.

 
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Scientific understanding is purely mathematical.

Maths is but a modeling tool kit we use to describe what we think and see. Pure maths has no purpose until it is applied, assigned an application with understanding from outside mathematics.

Personally I’m of the school of though that it is not possible to determine all the laws of the physical world. The model is simply too complex for us to comprehend and there are too many variables to account for. Whether or not there is something beyond the physical world effecting is a whole other dilemma, but we’ve got our hands full so lets ignore that.

A bit more on topic, like most people on this thread, I agree that a hybrid approach would be best. Near pure logic might have gotten us a long way, but we don’t have anything capable of that so we’ll have to find another way. Even if we were beings capable of purely logical thought, empirical evidence is needed for the law of non-contradiction to be of any use. Any law you derive by logic needs to be checked empirically. You need to look at your data to see whether or not your law is valid, but at the same time your law must not only seek to simply abide by the observations but to explain them.

Empiricism can bring with it the temptation to draw a regression line and think you have a law explaining a bit of your world but, by definition, you are merely predicting what you’ll see next based on what you have seen. Logic is required to understand your observations and deduce a law.

 
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Trying to understand your posts normally gives me an aneurysm, mxmm. Still I thought this article seems relevant to this topic and you might find it interesting. The End of Theory: The Data Deluge Makes the Scientific Method Obsolete