Schrödingers critisism of observation only applies on the quantum level, where observation by necessity also require influencing what one try to observe. Nonetheless the predictive nature of QM makes it so that we can observe the result without influencing the process and thus validate the model we have of the process. We cannot observe the process directly without influencing, just by the result it gives.
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Originally Posted by g0pher
1) Predicting ability: Science is based on regularities in nature, and cannot predict what is irregular. For example, we can predict movement of single particles, but cannot predict net movements in chaos theory.
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Partly true. More correct, currently true. If the model is correct, it is a question of computing power. Given enough computing power, in theory, anything can be simulated.
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Originally Posted by g0pher
2) Implementation of experiment: Some experiments are presently impossible to implement, like gathering physical samples from Neptune, or computing the movement of air particles in a room in REAL time. Limits in physical equipment, therefore, is the main problem.
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Same as above. A technological problem. These I am sure can be overcome with due time.
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Originally Posted by g0pher
3) Inductive nature: I think everyone should know Hume's argument, I won't go over it again. P.S. How do we know what we observe is only seemingly "true" and not really what happens? Ok, don't bother answering this, but it shows the problem in observational data gathering in the scientific method.
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Either one accept what we observe (and agree upon observing) as being real or one don't. That is not to say that what we observe may have deeper causation than what immidiatly meets the eye.
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Originally Posted by g0pher
4) Human intellect: Scientists are human - their thinking processes are clouded by background beliefs and biasness. Will this not affect their ability to "think out of the box" in creation of theories? This is why we do not have Einsteins popping up every other day.
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Confirmation bias is the one thing science is good at stamping out. But it do take time, and a good amount of evidense. Science like all other human endevaurs are prone to error, but science is self correcting. New ideas are not that easy to think up, but once it gains momentum...
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Originally Posted by g0pher
Does this mean that knowledge construction in Science will inevitably stagnate? When that happens, will the scientific method be outdated?
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The method by itself I do not think will get outdated anytime soon. But there is a problem with the ever increasing speciality of the sciences. Meaning new discoveries will more often need a collaboration between disciplines, a larger group of researches. Each with their own little pet-theories.
As such scientific knowledge will continue to grow as long as human culture do not regress.
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Originally Posted by g0pher
Will a new method of inquiry come to take its place in the world? Can a new scientific revolution open up yet more fields of scientific pursuits or is the scientific field already saturated?
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Possible; yes; no.
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Originally Posted by g0pher
Most importantly, is this method of thinking simply arising from my own inability to comprehend what I do not yet know, like a blind man's perception of light?
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Great way of putting it. Yes. Science opens new avenues of perception, today we can observe the entire EM spectrum. Not that long ago all we could observe was limited to that little piece of it known as visible light. But at the same time, the sciences are limited to current knowledge and technology. We cannot know what we cannot observe. Be that directly or indirectly.